M. Abadi, A Semantics for Static Type Inference in a Nondeterministic Language, Information and Computation, vol.109, issue.1-2, pp.300-306, 1994.
DOI : 10.1006/inco.1994.1019

S. Abramsky, On semantic foundations for applicative multiprogramming, ICALP'83, pp.1-14, 1983.
DOI : 10.1007/BFb0036893

S. Abramsky, R. Jagadeesan, and P. Malacaria, Full Abstraction for PCF, Information and Computation, vol.163, issue.2, pp.409-470, 2000.
DOI : 10.1006/inco.2000.2930

URL : http://doi.org/10.1006/inco.2000.2930

R. Amadio and P. Curien, Domains and lambda-calculi. Number 46 in Cambridge Tracts in Theoretical Computer Science, 1998.
DOI : 10.1017/cbo9780511983504

URL : https://hal.archives-ouvertes.fr/inria-00070008

A. Asperti and G. Longo, Categories, types and structures: an introduction to category theory for the working computer scientist, 1991.

J. Baeten and B. Boerboom, Omega can be anything it should not be, Proc. Koninklijke Netherlandse Akademie van Wetenschappen, Serie A, Indag. Matematicae 41, pp.111-120, 1979.
DOI : 10.1016/1385-7258(79)90016-7

URL : http://doi.org/10.1016/1385-7258(79)90016-7

H. P. Barendregt, The Type Free Lambda Calculus, Handbook of Mathematical Logic, pp.1091-1132, 1977.
DOI : 10.1016/S0049-237X(08)71129-7

H. P. Barendregt, The lambda calculus: its syntax and semantics. North- Holland, 1984.

H. P. Barendregt, M. Coppo, and M. Dezani-ciancaglini, A filter lambda model and the completeness of type assignment, The Journal of Symbolic Logic, vol.37, issue.04, pp.931-940, 1983.
DOI : 10.1002/malq.19800261902

]. O. Bastonero, Modèles fortement stables du ?-calcul et résultats d'incomplétude, Thèse de Doctorat, 1996.

O. Bastonero and X. Gouy, Strong stability and the incompleteness of stable models for ??-calculus, Annals of Pure and Applied Logic, vol.100, issue.1-3, pp.247-277, 1999.
DOI : 10.1016/S0168-0072(99)00015-9

S. Berardi and C. Berline, ????-complete models for System F, Mathematical Structures in Computer Science, vol.12, issue.06, pp.823-874, 2002.
DOI : 10.1017/S0960129502003778

C. Berline, From computation to foundations via functions and application: The ??-calculus and its webbed models, Theoretical Computer Science, vol.249, issue.1, pp.81-161, 2000.
DOI : 10.1016/S0304-3975(00)00057-8

C. Berline, Graph models of $\lambda$-calculus at work, and variations, Mathematical Structures in Computer Science, vol.16, issue.02, pp.1-37, 2006.
DOI : 10.1017/S0960129506005123

URL : https://hal.archives-ouvertes.fr/hal-00004473

C. Berline, G. Manzonetto, and A. Salibra, Lambda Theories of Effective Lambda Models, Proc. 16th EACSL Annual Conference on Computer Science and Logic (CSL'07), pp.268-282, 2007.
DOI : 10.1007/978-3-540-74915-8_22

URL : https://hal.archives-ouvertes.fr/hal-00125816

C. Berline and A. Salibra, Easiness in graph models, Theoretical Computer Science, vol.354, issue.1, pp.4-23, 2006.
DOI : 10.1016/j.tcs.2005.11.005

URL : https://hal.archives-ouvertes.fr/hal-00003751

G. Berry, Stable models of typed lambda-calculi, Proceedings of the Fifth Colloquium on Automata, Languages and Programming, 1978.

G. Berry, Modèlescompì etement adéquats et stable des ?-calculs typés, 1979.

G. Berry, On the definition of lambda-calculus models, Proc. Int, pp.218-230, 1981.
DOI : 10.1007/3-540-10699-5_99

URL : https://hal.archives-ouvertes.fr/inria-00076515

G. Berry, Some syntactic and categorical constructions of lambda-calculus models, 1981.
URL : https://hal.archives-ouvertes.fr/inria-00076481

G. Berry, P. Curien, and J. Lévy, Full Abstraction for sequential languages: the state of the art, Algebraic Methods in Semantics, pp.89-132, 1985.

D. Bigelow and S. Burris, Boolean algebras of factor congruences, Acta Sci. Math, vol.54, pp.11-20, 1990.

G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc, pp.433-454, 1935.

G. Boudol, Sémantique opérationnelle et algébrique des programmes récursifs non-déterministes, Thèse de Doctorat, pp.80-108, 1980.

A. Bucciarelli and T. Ehrhard, Sequentiality and strong stability, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science, pp.138-145, 1991.
DOI : 10.1109/LICS.1991.151638

A. Bucciarelli and T. Ehrhard, On phase semantics and denotational semantics: the exponentials, Annals of Pure and Applied Logic, vol.109, issue.3, pp.205-241, 2001.
DOI : 10.1016/S0168-0072(00)00056-7

URL : https://hal.archives-ouvertes.fr/hal-00527042

A. Bucciarelli, T. Ehrhard, and G. Manzonetto, Not Enough Points Is Enough, Proc. 16th EACSL Annual Conference on Computer Science and Logic (CSL'07), pp.298-312, 2007.
DOI : 10.1007/978-3-540-74915-8_24

URL : https://hal.archives-ouvertes.fr/hal-00148820

A. Bucciarelli and A. Salibra, The Minimal Graph Model of Lambda Calculus, MFCS'03, pp.300-307, 2003.
DOI : 10.1007/978-3-540-45138-9_24

URL : https://hal.archives-ouvertes.fr/hal-00149557

A. Bucciarelli and A. Salibra, The sensible graph theories of lambda calculus, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004., pp.276-285, 2004.
DOI : 10.1109/LICS.2004.1319622

URL : https://hal.archives-ouvertes.fr/hal-00149558

A. Bucciarelli and A. Salibra, Graph lambda theories, Mathematical Structures in Computer Science, vol.45, issue.05
DOI : 10.1016/0022-0000(92)90040-P

URL : https://hal.archives-ouvertes.fr/hal-00149556

S. Burris and H. P. Sankappanavar, A course in universal algebra, 1981.
DOI : 10.1007/978-1-4613-8130-3

S. Burris and H. Werner, Sheaf constructions and their elementary properties. Transactions of the, pp.269-309, 1979.
DOI : 10.1090/s0002-9947-1979-0522263-8

A. Church, A Set of Postulates for the Foundation of Logic, The Annals of Mathematics, vol.33, issue.2, pp.346-366, 1932.
DOI : 10.2307/1968337

A. Church, The calculi of lambda conversion, 1941.

S. Comer, Representations by algebras of sections over Boolean spaces, Pacific Journal of Mathematics, vol.38, issue.1, pp.29-38, 1971.
DOI : 10.2140/pjm.1971.38.29

D. Cooperstock, Alternative axiomatizations of models of lambda-calculus, 1981.

M. Coppo, M. Dezani-ciancaglini, F. Honsell, and G. Longo, Extended Type Structures and Filter Lambda Models, Logic Colloquium 82, pp.241-262, 1984.
DOI : 10.1016/S0049-237X(08)71819-6

M. Coppo, M. Dezani-ciancaglini, and M. Zacchi, Type theories, normal forms and D ? -lambda-models. Information and computation, pp.85-116, 1987.

M. Coppo, M. Dezani-ciangaglini, and B. Venneri, Principal type schemes and ?-calculus semantics, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp.535-560, 1980.

R. David, Computing with Böhm trees, Fundam. Inform, vol.45, issue.12, pp.53-77, 2001.

U. De-'liguoro and A. Piperno, Non deterministic extensions of untyped lambda-calculus, Inf. Comput, vol.122, issue.2, pp.149-177, 1995.

M. Dezani-ciancaglini, U. De-'liguoro, and A. Piperno, A Filter Model for Concurrent $\lambda$-Calculus, SIAM Journal on Computing, vol.27, issue.5, pp.1376-1419, 1998.
DOI : 10.1137/S0097539794275860

M. Dezani-ciancaglini and I. Margaria, A characterization of F-complete type assignments, Theoretical Computer Science, vol.45, issue.2, pp.121-157, 1986.
DOI : 10.1016/0304-3975(86)90043-5

P. , D. Gianantonio, G. Franco, and F. Honsell, Game semantics for untyped lambda calculus, Proc. of the conference Typed Lambda Calculus and Applications, pp.114-128, 1999.

P. , D. Gianantonio, F. Honsell, and G. Plotkin, Uncountable limits and the lambda calculus, Nordic Journal of Computing, vol.2, issue.2, pp.126-145, 1995.

E. Engeler, Algebras and combinators, Algebra Universalis, vol.13, issue.1, pp.389-392, 1981.
DOI : 10.1007/BF02483849

M. H. Escardó, PCF extended with real numbers, Theoretical Computer Science, vol.162, issue.1, pp.79-115, 1996.
DOI : 10.1016/0304-3975(95)00250-2

G. Franco, Some intensional model of lambda calculus, 2001.

P. Giannini and G. Longo, Effectively given domains and lambda-calculus models, Information and Control, vol.62, issue.1, pp.36-63, 1984.
DOI : 10.1016/S0019-9958(84)80009-1

URL : http://doi.org/10.1016/s0019-9958(84)80009-1

J. Girard, The system F of variable types, fifteen years later. Theoretical computer science, pp.159-192, 1986.

J. Girard, Normal functors, power series and the ?-calculus. Annals of pure and applied logic, pp.129-177, 1988.

X. Gouy, Etude des théoriesthéorieséquationnelles et des propriétés algébriques des modèles stables du ?-calcul, Thèse, 1995.

A. Gruchalski, Computability on dI-Domains, Information and Computation, vol.124, issue.1, pp.7-19, 1996.
DOI : 10.1006/inco.1996.0002

URL : http://doi.org/10.1006/inco.1996.0002

M. C. Hennessy and E. A. Ashcroft, A mathematical semantics for a nondeterministic typed lambda-calculus. Theoretical computer science, pp.227-245, 1980.

R. Hindley and G. Longo, Lambda-Calculus Models and Extensionality, Zeitschrift f??r Mathematische Logik und Grundlagen der Mathematik, vol.5, issue.19-21, pp.289-310, 1980.
DOI : 10.1002/malq.19800261902

F. Honsell and S. Rocca, An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus, Journal of Computer and System Sciences, vol.45, issue.1, pp.49-75, 1992.
DOI : 10.1016/0022-0000(92)90040-P

J. M. Hyland, A Syntactic Characterization of the Equality in Some Models for the Lambda Calculus, Journal of the London Mathematical Society, vol.2, issue.3, pp.361-37076, 1975.
DOI : 10.1112/jlms/s2-12.3.361

J. M. Hyland, M. Nagayama, J. Power, and G. Rosolini, A Category Theoretic Formulation for Engeler-style Models of the Untyped ??-Calculus, Electronic Notes in Theoretical Computer Science, vol.161, pp.43-57, 2006.
DOI : 10.1016/j.entcs.2006.04.024

J. M. Hyland and C. L. Ong, On full abstraction for PCF: I, II, and III. Information and Computation, pp.285-408, 2000.
DOI : 10.1006/inco.2000.2917

URL : http://doi.org/10.1006/inco.2000.2917

Y. Jiang, Consistence et inconsistence de théories de ?-calcuí etendus, Thèse, 1993.

P. T. Johnstone, Stone spaces, 1982.

J. L. Kelley, General topology, 1955.

A. D. Ker, H. Nickau, and C. L. Ong, A universal innocent game model for the Böehm tree lambda theory, Computer Science Logic: Proceedings of the 8th Annual Conference on the EACSL, pp.405-419, 1999.

R. Kerth, 2 ? 0 modèles de graphes nonéquationnellementéquivalentsnonéquationnellementnonéquationnellementéquivalents, Notes de comptes-rendus de l'Academie des Sciences, pp.587-590, 1994.

R. Kerth, Isomorphism etéquivalencéetéquivalencé equationnelle entre modèles du ?-calcul, Thèse, 1995.

R. Kerth, The interpretation of unsolvable terms in models of pure ?-calculus

R. Kerth, Isomorphism and equational equivalence of continuous lambda models, Studia Logica, vol.61, issue.3, pp.403-415, 1998.
DOI : 10.1023/A:1005018121791

R. Kerth, On the construction of stable models of untyped ??-calculus, Theoretical Computer Science, vol.269, issue.1-2, pp.23-46, 2001.
DOI : 10.1016/S0304-3975(00)00371-6

C. P. Koymans, Models of the lambda calculus, Information and Control, vol.52, issue.3, pp.306-332, 1982.
DOI : 10.1016/S0019-9958(82)90796-3

J. Krivine, Lambda-calculus, types and models, 1990.
URL : https://hal.archives-ouvertes.fr/cel-00574575

J. Lambek, From ?-calculus to Cartesian closed categories, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp.375-402, 1980.

J. Lambek and P. J. Scott, Introduction to higher order categorical logic, volume 007 of Cambridge studies in advanced mathematics, 1986.

G. Longo, Set-theoretical models of ??-calculus: theories, expansions, isomorphisms, Annals of Pure and Applied Logic, vol.24, issue.2, pp.153-188, 1983.
DOI : 10.1016/0168-0072(83)90030-1

S. Lusin and A. Salibra, The Lattice of Lambda Theories, Journal of Logic and Computation, vol.14, issue.3, pp.373-394, 2004.
DOI : 10.1093/logcom/14.3.373

S. and M. Lane, Categories for the working mathematician. Number 5 in Graduate Texts in Mathematics, 1971.

G. Manzonetto and A. Salibra, Boolean Algebras for Lambda Calculus, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), pp.139-148, 2006.
DOI : 10.1109/LICS.2006.16

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.9637

R. N. Mckenzie, G. F. Mcnulty, and W. F. Taylor, Algebras, lattices, varieties, Volume I, 1987.

A. R. Meyer, What is a model of the lambda calculus? Information and Control, pp.87-122, 1982.

P. Odifreddi, Classical Recursion Theory, 1989.

C. L. Ong, Non-determinism in a functional setting, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science, pp.275-286, 1993.
DOI : 10.1109/LICS.1993.287580

R. S. Pierce, Modules over commutative regular rings. Memoirs Amer, Math. Soc, 1967.

D. Pigozzi and A. Salibra, Lambda abstraction algebras: coordinatizing models of lambda calculus, Fundam. Inf, vol.33, issue.2, pp.149-200, 1998.

G. D. Plotkin, A set-theoretical definition of application, School of artificial intelligence, 1971.

G. D. Plotkin, The ?-calculus is ?-incomplete. The Journal of Symbolic Logic, pp.313-317, 1974.

G. D. Plotkin, LCF considered as a programming language, Theoretical Computer Science, vol.5, issue.3, pp.223-255, 1977.
DOI : 10.1016/0304-3975(77)90044-5

G. D. Plotkin, T?? as a Universal Domain, Journal of Computer and System Sciences, vol.17, issue.2, pp.209-236, 1978.
DOI : 10.1016/0022-0000(78)90006-5

G. D. Plotkin, Set-theoretical and other elementary models of the ??-calculus, Theoretical Computer Science, vol.121, issue.1-2, pp.351-409, 1993.
DOI : 10.1016/0304-3975(93)90094-A

A. Salibra, On the algebraic models of lambda calculus, Theoretical Computer Science, vol.249, issue.1, pp.197-240, 2000.
DOI : 10.1016/S0304-3975(00)00059-1

A. Salibra, A continuum of theories of lambda calculus without semantics, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science, pp.334-343, 2001.
DOI : 10.1109/LICS.2001.932509

A. Salibra, Topological incompleteness and order incompleteness of the lambda calculus, LICS'01 Special Issue, number 4 in ACM Transactions on Computational Logic, pp.379-401, 2003.
DOI : 10.1145/772062.772067

M. Schönfinkel, Uber die bausteine der mathematischen logik (english translation in J. van Heijenoort ed.'s book " From Frege to Gödel, a source book in Mathematical Logic, pp.1879-1931, 1924.

D. Scott, Domains for denotational semantics, Proceedings of the Ninth International Colloquium on Automata , Languages and Programming, pp.577-613, 1982.
DOI : 10.1007/BFb0012801

D. S. Scott, Continuous lattices, Toposes, algebraic geometry and logic, 1972.
DOI : 10.1007/BFb0073967

D. S. Scott, The language LAMBDA (abstract), J. symbolic logic, vol.39, pp.425-427, 1974.

D. S. Scott, Lambda Calculus: Some Models, Some Philosophy, The Kleene Symposium, pp.223-265, 1980.
DOI : 10.1016/S0049-237X(08)71262-X

D. S. Scott, Relating theories of the ?-calculus, To H.B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalisms, pp.403-450, 1980.

P. Selinger, Order-incompleteness and finite lambda models, extended abstract, LICS '96: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, p.432, 1996.
DOI : 10.1109/lics.1996.561459

P. Selinger, Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms, 1997.

P. Selinger, The lambda calculus is algebraic, Journal of Functional Programming, vol.12, issue.06, pp.549-566, 2002.
DOI : 10.1017/S0956796801004294

P. Selinger, Order-incompleteness and finite lambda reduction models, Theoretical Computer Science, vol.309, issue.1-3, pp.43-63, 2003.
DOI : 10.1016/S0304-3975(02)00038-5

URL : http://doi.org/10.1016/s0304-3975(02)00038-5

V. Stoltenberg-hansen, I. Lindström, and E. R. Griffor, Mathematical theory of domains, 1994.
DOI : 10.1017/CBO9781139166386

A. M. Turing, The ??-function in ??-K-conversion, The Journal of Symbolic Logic, vol.57, issue.04, pp.164-164, 1937.
DOI : 10.1215/S0012-7094-36-00227-2

D. Vaggione, V with factorable congruences and V = I? a (V DI ) imply V is a discriminator variety, Acta Sci. Math, vol.62, pp.359-368, 1996.

D. Vaggione, Varieties in Which the Pierce Stalks Are Directly Indecomposable, Journal of Algebra, vol.184, issue.2, pp.424-434, 1996.
DOI : 10.1006/jabr.1996.0268

A. Visser, Numerations, ?-calculus, and arithmetic, Essays on Combinatory Logic, Lambda-Calculus, and Formalism, pp.259-284, 1980.

C. P. Wadsworth, The Relation between Computational and Denotational Properties for Scott???s ${\text{D}}_\infty $-Models of the Lambda-Calculus, SIAM Journal on Computing, vol.5, issue.3, pp.488-521, 1976.
DOI : 10.1137/0205036