# Questions tagged [lo.logic]

first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.

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### Concerning the various proofs from the axiom of choice that R^3 admits of surprising geometrical decompositions into circles, skew lines and so on: can we prove in any instance that there are no Borel such decompositions? Or that AC is required?

**32**

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### Peano Arithmetic and the Field of Rationals

**28**

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### Where do uncountable models collapse to?

**25**

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### Supercompact and Reinhardt cardinals without choice

**24**

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### Can one divide by the cardinal of an amorphous set?

**24**

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### Decidability of equality of elementary expressions

**24**

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### Defining $\mathbb{Z}$ in $\mathbb{Q}$

**21**

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### CH and automorphisms of ultrapowers of $\mathbb{Z}$ and $\mathbb{R}$

**21**

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### Relative null-ness

**20**

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### Density of first-order definable sets in a directed union of finite groups

**19**

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### Is Feferman's unlimited category theory dead?

**19**

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### Can Gentzen-style proofs give omega-consistency and beyond?

**18**

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### Is this Variation of the Continuum Hypothesis Inconsistent with ZFC or ZF?

**18**

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### Souslin trees on the first inaccessible cardinal

**18**

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### Hrushovski's Construction

**18**

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### Antichains of Cardinals in ZF Without Choice…

**17**

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### Rigid Non-archimedean Real Closed Fields

**17**

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### Is it consistent with ZF that $V\to V^{\ast \ast}$ is always surjective?

**17**

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### Does the pointclass of universally Baire sets always have the uniformization property?

**17**

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### What is the Cantor-Bendixson rank of the space of first order theories?

**17**

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### Souslin trees and weakly compact cardinals

**17**

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### Are there lightweight foundations for arbitrarily extendable objects?

**16**

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### Gitik's work on Shelah's weak hypothesis

**16**

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### Ramsey's theorem for the first uncountable ordinal

**16**

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### Gap two Sierpinski set?

**16**

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### Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?

**16**

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### Decidability of $x^3+y^3+z^3 = c$

**16**

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### Ideas behind Gitik's solution of PCF conjecture

**15**

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### What is the smallest unsolved diophantine equation?

**15**

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### The axiom $I_0$ in the absence of $AC$

**15**

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### Minimal resources for Undecidability of First-Order Logic: the number of variables

**15**

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### To what extent does (co)homology of groups made discrete depend on set theory?

**14**

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### O-minimality and forcing

**14**

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### The failure of GCH al $\aleph_\omega$ by nice forcing

**14**

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### Complexity classes for BSS machines

**14**

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### Adding a saturated ideal

**14**

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### Has anyone read/debunked Yessenin-Volpin–Hennix “Beware of the Gödel-Wette paradox”?

**14**

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### What is the simplest known arithmetic definition of exponentiation?

**13**

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### Cardinality vs. isomorphism type of vector spaces without choice

**13**

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### What is the logical complexity of the Hodge conjecture?

**13**

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### Constructing a topos from a Heyting algebra

**13**

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### Algebraic proofs of algebraic theorems about algebraically closed fields

**13**

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### If $U,D$ are $\kappa$-complete nonprincipal ultrafilters on $\kappa$ and $j_U(U) = j_D(D)$, is $U=D$?

**13**

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### Is the universality of the surreal number line a weak global choice principle?

**13**

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### The topos for forcing in computability theory

**13**

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### How to measure the strength of Zermelo over bounded Zermelo?

**13**

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### Does Fermat hold in non-standard models?

**12**

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### A question concerning model theory of groups

**12**

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### Can you define a probability measure on the set of countable transitive models of ZFC?

**12**

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