# 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.

**1**

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### Is there a foundational approach that takes “structure” as primitive?

**3**

**2**answers

### A ‘canonical’ bounded lattice with proper de Morgan negation?

**4**

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### What's the smallest $\lambda$-calculus term not known to have a normal form?

**5**

**1**answer

### Every complex number has a square root via LLPO without weak countable choice

**2**

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### Can we have the well founded world of NF obeying ZF?

**6**

**1**answer

### Internal vs. external definability of inner models

**-1**

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### If it is possible to define the Busy Beaver function for Hypermachines ($\Sigma_n$-machines of arbitrary $n>2$), how “strong” such a function will be?

**1**

**1**answer

### The “higher topology” of countable Scott sets

**5**

**1**answer

### What types are to mathematical proofs as types à la Martin-Löf are to constructive proofs, and what's wrong with them?

**2**

**0**answers

### A decision problem from sheaf set theory?

**1**

**1**answer

### Non-relativized, Computable and Schnor randomness w.r.t a measure

**0**

**1**answer

### Kurtz randomness and supermartingales with infinite *limit*

**0**

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### Are there minor tweaks of hereditary replacement that can prove large cardinal properties?

**8**

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### Topology is to semi-decidability, coarse structures are to what?

**0**

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### Is there a standard way to relativize algorithmic complexity constructively?

**0**

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### Could this intended maximal anti-foundation axiom result in increment of consistency strength over that of ZFC?

**7**

**1**answer

### Bounding and domination numbers for relation $\leq$ modulo $\omega$-nullsets

**0**

**1**answer

### Can we have cyclic generalized positive comprehension?

**20**

**2**answers

### Could groups be used instead of sets as a foundation of mathematics?

**0**

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### Is this anti-foundation axiom consistent?

**-1**

**1**answer

### Is cyclic replacement inconsistent with ZFC-Foundation?

**8**

**0**answers

### *Really* undetermined Banach-Mazur games?

**0**

**0**answers

### Satisfying systems in Gödel's original proof of completeness

**10**

**1**answer

### Does $Π^1_{2n+1} = (Σ^1_{2n+1})^{M_{2n-1}}$?

**3**

**0**answers

### Is there a second-order expression of '$\kappa$ is Reinhardt' in $NGB$, where $\kappa$ is a cardinal?

**1**

**0**answers

### Can small class choice be weaker than global choice and stronger than set choice + collection?

**5**

**0**answers

### General theory of the reals in Solovay-like models

**9**

**1**answer

### Logical completeness of Hilbert system of axioms

**-1**

**1**answer

### Is Proper Class Choice equivalent to Global Choice?

**22**

**2**answers

### Undetermined Banach-Mazur games in ZF?

**0**

**1**answer

### Set of definable real numbers?

**0**

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### What's the strength of capturing set theory in labeled Mereology?

**-2**

**1**answer

### Does MK prove internally that there are more proper classes than sets?

**-1**

**1**answer

### Weak power set - what strength may it have?

**6**

**0**answers

### $0^\#$ in weak theories vs large cardinals in $L$

**0**

**0**answers

### Reference Request: Had that Labeled-Mereological system been studied before?

**1**

**0**answers

### A countable set theory providing choice?

**1**

**0**answers

### Is there a restrain on the total number of proper classes strictly smaller than the universe in variants of MK?

**5**

**1**answer

### Self-embeddings of uncountable total orders, 2

**6**

**0**answers

### How bad a proper forcing of size $\aleph_1$ can be?

**9**

**1**answer

### Is there a ring for which the reducibility of a polynomial is undecidable?

**4**

**1**answer

### Forcing square introduces diamond

**3**

**0**answers

### Improving a Lindstrom-y fact about $\mathcal{L}_{\omega_1,\omega}$?

**3**

**0**answers

### Elementary self-embeddings conservative over ZFC

**6**

**1**answer

### Is $\prod_{X : \mathcal{U}} (X \to X) \cong 1$ consistent with type theory?

**5**

**1**answer

### Can $H_{\omega_1}$ and $H_{\omega_2}$ be in bi-interpretation synonymy?

**1**

**1**answer

### Is every true $\Pi^0_1$ statement entailed from a consistency statement of $PA$?

**1**

**1**answer

### Category of finite models of a $\tau$-sentence

**6**

**1**answer

### “Robinson arithmetic” for (some) levels of $L$?

**0**

**0**answers