# 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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### What is the consistency strength of this kind of reflection principle?

**4**

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### A strong plus-one hypothesis

**1**

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### Semantics/Syntax distinction vs. Meta/Object language distinction

**1**

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### Can we have a theory $T$ that is complete for simple sentences in the language of $T$ that are weaker than $ Con(T)$?

**15**

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### What is the smallest unsolved diophantine equation?

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### Differences between logic with and without equality

**7**

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### Destroying Suslin, nothing special

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### Is “ZF+ V=L” an upper limit theory for cardinal decidability (per its strength)?

**3**

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### What are the definable sets in Skolem arithmetic?

**2**

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### Meta-incomputability

**3**

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### Formal foundations done properly [closed]

**5**

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### van der Waerden's theorem in Reverse Mathematics

**7**

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### Does $\mathsf{MA}^+(\sigma-{\rm closed})$ imply there are no Kurepa Trees?

**1**

**1**answer

### What is the strength of this strict constructible iterative hierarchy?

**2**

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### Conservativity of language extension

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### Is Replacement motivated by ranked iterative conception of sets?

**12**

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### A peculiarity of Henkin's 1950 proof of completeness for higher order logic

**16**

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### Is there a pair of non-isomorphic structures each of which is isomorphic to an ultrapower of the other?

**4**

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### Reference request: destroying saturation at an inaccessible?

**8**

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### Primitive recursive and feasible presentations for nonstandard models of arithmetic

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### Can MK be interpreted in a class theory about an abstract hierarchy principle + an accessibility principle?

**6**

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### Action of infinite symmetric groups on iterated power sets

**2**

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### If Goldbach's Conjecture is eventually true, is it necessarily true?

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### Probably true, but provably unprovable

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### What happens when you iterate Cohen reals?

**8**

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### Is there a version of the “infinitary” disjunctive normal form theorem for topoi and slice categories?

**10**

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### Looking for “Set theory for a small universe” by Ketonen

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### Formula orderings in infinite propositional logic and existence of minimum

**13**

**1**answer

### reverse mathematics of the Lebesgue measurability of analytic sets

**10**

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### stationary reflection in $[\kappa]^\omega$

**6**

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### Singular strong generator

**3**

**1**answer

### Function $f:\kappa\to\alpha$ with small fibers where $\alpha\in\kappa$

**3**

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### What is the dual of generating Boolean subalgebra by subexpressions of a modal formula?

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### O-minimality and forcing

**5**

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### Characterizing “bounded” distributivity in terms of dense open sets

**4**

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### bijections and order types

**1**

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### Does Regularity schema imply $\in$-induction when added to first order Zermelo set theory?

**8**

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### Is there an expansion of $(\mathbb{N},+,<)$ by a pairing function that is still NIP?

**1**

**1**answer

### The continuum hypothesis and the diamond principle for $\aleph_1$

**2**

**1**answer

### Is $\in$-induction provable in first order Zermelo set theory?

**5**

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### Natural examples of recursive pseudowellorderings

**4**

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### Ordinal analysis and nonrecursive ordinals

**5**

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### Progress towards a computational interpretation of the univalence axiom?

**10**

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### Relation between the Axiom of Choice and a the existence of a hyperplane not containing a vector

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### Is there a known shorter axiomatization of NF than this?

**1**

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### Reduction of the predicate calculus to the propositional calculus in the case of one sigle object in the universe? [closed]

**3**

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### If any satisfiable $\mathcal{L}_{κ,κ}(Q_{=κ})$-theory remains satisfiable when replacing $Q_{=κ}$ with $Q_{=μ}$, is $κ$ huge?

**7**

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### Can we inductively define Wadge-well-foundedness?

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### Functoriality of indiscernible sequences

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