A model of second-order arithmetic satisfying AC but not DC

DOI10.1142/S0219061318500137zbMath1484.03067arXiv1808.04732MaRDI QIDQ5223119

Kanovei, Vladimir, Victoria Gitman, Sy-David Friedman

Publication date: 8 July 2019

Published in: Journal of Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04732

zbMATH Keywords

independencesecond-order arithmeticchoice-schemedependent choice-scheme

Mathematics Subject Classification ID

Consistency and independence results (03E35) Models of arithmetic and set theory (03C62) Second- and higher-order arithmetic and fragments (03F35) Axiom of choice and related propositions (03E25)

Related Items (9)

On Russell typicality in set theory ⋮ Models of set theory in which the separation theorem fails ⋮ On the ‘definability of definable’ problem of Alfred Tarski, Part II ⋮ TAKING REINHARDT’S POWER AWAY ⋮ THE Σ₁-DEFINABLE UNIVERSAL FINITE SEQUENCE ⋮ The full basis theorem does not imply analytic wellordering ⋮ A good lightface \(\varDelta_n^1\) well-ordering of the reals does not imply the existence of boldface \(\mathbf{\Delta}_{n - 1}^1\) well-orderings ⋮ INITIAL SELF-EMBEDDINGS OF MODELS OF SET THEORY ⋮ Boolean-valued class forcing

Cites Work

• A countable definable set containing no definable elements
• What is the theory without power set?
• [https://portal.mardi4nfdi.de/wiki/Publication:3328537 A Minimal Model for � CH: Iteration of Jensen's Reals]
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