Issues

$\Delta_1$ presentation of the uniform reflection schema

FormalizedFormalLogic/AlphaCentauri#242 · opened

on Sep 17, 2026

$\Sigma_0(\Sigma_n)$ predicates are $\Delta_{n+1}$

FormalizedFormalLogic/AlphaCentauri#241 · opened

on Sep 17, 2026

The class $\Sigma_0(\Sigma_n)$

FormalizedFormalLogic/AlphaCentauri#240 · opened

on Sep 17, 2026

Strong $\Sigma_n$ collection from piecewise coding

FormalizedFormalLogic/AlphaCentauri#239 · opened

on Sep 17, 2026

$\Delta_1$ induction proves $\mathsf{B}\Sigma_1$ over $\mathsf{EA}$

FormalizedFormalLogic/AlphaCentauri#237 · opened

on Sep 17, 2026

The limit sequence is not coded

FormalizedFormalLogic/AlphaCentauri#236 · opened

on Sep 17, 2026

The $\Sigma_1$ cut of an enumeration

FormalizedFormalLogic/AlphaCentauri#235 · opened

on Sep 17, 2026

An injective enumeration from a failure of $\mathsf{B}\Sigma_1$

FormalizedFormalLogic/AlphaCentauri#234 · opened

on Sep 17, 2026

The pigeonhole principle for coded injections

FormalizedFormalLogic/AlphaCentauri#233 · opened

on Sep 17, 2026

Block-coded sequences over $\mathsf{EA}$

FormalizedFormalLogic/AlphaCentauri#232 · opened

on Sep 17, 2026

Proper cuts as counterexamples to induction

FormalizedFormalLogic/AlphaCentauri#231 · opened

on Sep 17, 2026

Strict definability with parameters

FormalizedFormalLogic/AlphaCentauri#230 · opened

on Sep 17, 2026

$\Delta_{n+1}$ induction proves $\mathsf{B}\Sigma_{n+1}$ over $\mathsf{EA}$

FormalizedFormalLogic/AlphaCentauri#226 · opened

on Sep 17, 2026

Unboundedness of parameter-free induction

FormalizedFormalLogic/AlphaCentauri#217 · opened

on Sep 16, 2026

Parameter-free $\Pi_{n+1}$ induction as relativized local reflection

FormalizedFormalLogic/AlphaCentauri#216 · opened

on Sep 16, 2026

$\Pi_{n+1}$-conservativity over iterated uniform reflection

FormalizedFormalLogic/AlphaCentauri#214 · opened

on Sep 16, 2026

$\mathcal{B}(\Sigma_{n+1})$-conservativity of local reflection

FormalizedFormalLogic/AlphaCentauri#213 · opened

on Sep 16, 2026

Iterated uniform $\Pi_n$ reflection

FormalizedFormalLogic/AlphaCentauri#211 · opened

on Sep 16, 2026

Relativized local reflection on Boolean combinations

FormalizedFormalLogic/AlphaCentauri#210 · opened

on Sep 16, 2026

Derivability conditions for relativized provability

FormalizedFormalLogic/AlphaCentauri#209 · opened

on Sep 16, 2026

1

The hierarchy of fragments $\mathsf{I}\Sigma_n$, $\mathsf{B}\Sigma_n$ and $\mathsf{L}\Sigma_n$

FormalizedFormalLogic/AlphaCentauri#124 · opened

on Sep 7, 2026

$\mathsf{I}\Sigma_n$ is strictly weaker than $\mathsf{B}\Sigma_{n+1}$

FormalizedFormalLogic/AlphaCentauri#123 · opened

on Sep 7, 2026

$\mathsf{B}\Sigma_{n+1}$ is strictly weaker than $\mathsf{I}\Sigma_{n+1}$

FormalizedFormalLogic/AlphaCentauri#122 · opened

on Sep 7, 2026

Internal soundness of interpretations

FormalizedFormalLogic/AlphaCentauri#83 · opened

on Sep 5, 2026

Interpretability of $T + \neg\mathrm{Con}_T$ in $T$

FormalizedFormalLogic/AlphaCentauri#82 · opened

on Sep 5, 2026

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Issues

$\Delta_1$ presentation of the uniform reflection schema

$\Sigma_0(\Sigma_n)$ predicates are $\Delta_{n+1}$

The class $\Sigma_0(\Sigma_n)$

Strong $\Sigma_n$ collection from piecewise coding

$\Delta_1$ induction proves $\mathsf{B}\Sigma_1$ over $\mathsf{EA}$

The limit sequence is not coded

The $\Sigma_1$ cut of an enumeration

An injective enumeration from a failure of $\mathsf{B}\Sigma_1$

The pigeonhole principle for coded injections

Block-coded sequences over $\mathsf{EA}$

Proper cuts as counterexamples to induction

Strict definability with parameters

$\Delta_{n+1}$ induction proves $\mathsf{B}\Sigma_{n+1}$ over $\mathsf{EA}$

Unboundedness of parameter-free induction

Parameter-free $\Pi_{n+1}$ induction as relativized local reflection

$\Pi_{n+1}$-conservativity over iterated uniform reflection

$\mathcal{B}(\Sigma_{n+1})$-conservativity of local reflection

Iterated uniform $\Pi_n$ reflection

Relativized local reflection on Boolean combinations

Derivability conditions for relativized provability

The hierarchy of fragments $\mathsf{I}\Sigma_n$, $\mathsf{B}\Sigma_n$ and $\mathsf{L}\Sigma_n$

$\mathsf{I}\Sigma_n$ is strictly weaker than $\mathsf{B}\Sigma_{n+1}$

$\mathsf{B}\Sigma_{n+1}$ is strictly weaker than $\mathsf{I}\Sigma_{n+1}$

Internal soundness of interpretations

Interpretability of $T + \neg\mathrm{Con}_T$ in $T$