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Logic and Foundations

Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set theory and beyond. For example, the principle of clopen determinacy for proper class games is exactly equivalent to the principle of elementary transfinite recursion ETR, strictly between GBC and GBC+$\Pi^1_1$-comprehension; open determinacy for class games, in contrast, is strictly stronger; meanwhile, the class forcing theorem, asserting that every class forcing notion admits corresponding forcing relations, is strictly weaker, and is exactly equivalent to the fragment $\text{ETR}_{\text{Ord}}$ and to numerous other natural principles. What is emerging is a higher set-theoretic analogue of the familiar reverse mathematics of second-order number theory. Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set theory and beyond. For example, the principle of clopen determinacy for proper class games is exactly equivalent to the principle of elementary transfinite recursion ETR, ...

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Documents 03E30 | enregistrements trouvés : 19

The hierarchy of second-order set theories between GBC and KM and beyond Hamkins, Joel David | CIRM H Nouveau

Axiomatic set-theoryimpredicative theories of classes Chuaqui, Rolando Basim | North-Holland Publishing Co. 1981 Nouveau

A formalization of set theory without variables Tarski, Alfred ; Givant, Steven | American Mathematical Society 1987 Nouveau

Axiomatic set theory Bernays, Paul ; Fraenkel, A. A. | North-Holland Publishing Co. 1968 Nouveau

Six papers in logic Artemov, S. N. ; Bekenov, M. I. ; Korshunov, A. D. | American Mathematical Society 1987 Nouveau

La méthode axiomatique :conférence de la réunion internationale de mathématiciens, tenue à Paris en Juillet 1937 Gonseth, F. | Gauthier-Villars 1938 Nouveau

Analyse Ithéorie des ensembles et topologie Schwartz, Laurent ; Zizi, K. | Hermann 1991 Nouveau

Real analysis and probability Dudley, R. M. | Cambridge University Press;Chapman & Hall 1989 Nouveau

Sets and classes :on the work by Paul Bernays Muller, G. H. | North-Holland Publishing Co. 1976 Nouveau

Discovering modern set theory. I :the basics Just, Winfried ; Weese, Martin | American Mathematical Society 1996 Nouveau

The foundations of mathematics in the theory of sets Mayberry, J. P. | Cambridge University Press 2000 Nouveau

Logique mathématique. Tome 2 :fonctions récursives, théorème de Gödel, théorie des ensembles, théorie des modèles Cori, René ; Lascar, Daniel ; Krivine, J. L. | Dunod 2003 Nouveau

Axiomatic set theory Suppes, Patrick | D. Van Nostrand Co. Inc. 1967 Nouveau

Notes on set theory Moschovakis, Yiannis N. | Springer 2006 Nouveau

Ernst Zermelo : Collected Works, Volume I : Set Theory, Miscellanea Zermelo, Ernst ; Ebbinghaus, Heinz-Deiter ; Fraser, Craig G. ; Kanamori, Akihiro | Springer 2010 Nouveau

A course on set theory Schimmerling, Ernest | Cambridge University Press 2011 Nouveau

Combinatorial set theory:with a gentle introduction to forcing Halbeisen, Lorenz J. | Springer 2012 Nouveau

La théorie des ensembles :introduction à une théorie de l'infini et des grands cardinaux Dehornoy, Patrick | Calvage & Mounet 2017 Nouveau

Hilbert’s tenth problem:an introduction to logic, number theory, and computability Murty, M. Ram ; Fodden, Brandon | American Mathematical Society 2019 Nouveau

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Axiomatic set-theory
impredicative theories of classes Chuaqui, Rolando Basim | North-Holland Publishing Co. 1981 Nouveau

La méthode axiomatique :
conférence de la réunion internationale de mathématiciens, tenue à Paris en Juillet 1937 Gonseth, F. | Gauthier-Villars 1938 Nouveau

Analyse I
théorie des ensembles et topologie Schwartz, Laurent ; Zizi, K. | Hermann 1991 Nouveau

Sets and classes :
on the work by Paul Bernays Muller, G. H. | North-Holland Publishing Co. 1976 Nouveau

Discovering modern set theory. I :
the basics Just, Winfried ; Weese, Martin | American Mathematical Society 1996 Nouveau

Logique mathématique. Tome 2 :
fonctions récursives, théorème de Gödel, théorie des ensembles, théorie des modèles Cori, René ; Lascar, Daniel ; Krivine, J. L. | Dunod 2003 Nouveau

Combinatorial set theory:
with a gentle introduction to forcing Halbeisen, Lorenz J. | Springer 2012 Nouveau

La théorie des ensembles :
introduction à une théorie de l'infini et des grands cardinaux Dehornoy, Patrick | Calvage & Mounet 2017 Nouveau

Hilbert’s tenth problem:
an introduction to logic, number theory, and computability Murty, M. Ram ; Fodden, Brandon | American Mathematical Society 2019 Nouveau