Question

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

score 100 · Answer 1 · 2026-02-23 12:06:38

100

Views

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

Published on 23 Feb 2026 - 12:06

score 64 · Answer 2 · 2026-04-09 11:18:36

64

Views

Proof in Natural Deduction, Sequent Calculus or Hilbert System

Published on 09 Apr 2026 - 11:18

score 93 · Answer 3 · 2026-02-23 12:01:18

93

Views

Is there a G4ip equivalent for first-order logic?

Published on 23 Feb 2026 - 12:01

score 60 · Answer 4 · 2026-02-23 12:05:34

60

Views

Reflection principle for finite subsystems of PA.

Published on 23 Feb 2026 - 12:05

score 67 · Answer 5 · 2026-02-23 12:03:00

67

Views

Establishing $\Gamma, A: Type \vdash (A)Type\ \textbf{kind}$ in LF

Published on 23 Feb 2026 - 12:03

score 34 · Answer 6 · 2026-02-23 12:06:36

34

Views

Equivalence of Martin-Löf sequent calculus and standard sequent calculus with material implications

Published on 23 Feb 2026 - 12:06

score 40 · Answer 7 · 2026-02-23 12:04:17

40

Views

Sequents in which succedents are restricted to one formula

Published on 23 Feb 2026 - 12:04

score 86 · Answer 8 · 2026-02-23 12:06:36

86

Views

Is there some variant of sequent calculus that allows for non-trivial axioms?

Published on 23 Feb 2026 - 12:06

score 96 · Answer 9 · 2026-02-23 12:05:45

96

Views

Exchange case in proving interpolation theorem by induction on the length of proof tree

Published on 23 Feb 2026 - 12:05

score 44 · Answer 10 · 2026-02-23 12:09:14

44

Views

What is the correct way to interpret the Intuitionistic rules of Kleene's sequent (Gentzen) system G1 (in sec. 77 of Kleene I.M. 1952)

Published on 23 Feb 2026 - 12:09

score 126 · Answer 11 · 2026-02-23 12:06:23

126

Views

What is the metatheory required for proving the cut-elimination theorem for classical logic? Is the proof circular?

Published on 23 Feb 2026 - 12:06

score 39 · Answer 12 · 2026-02-23 11:59:36

39

Views

Understanding quantifier rules in sequent calculus

Published on 23 Feb 2026 - 11:59

score 171 · Answer 13 · 2026-02-23 12:08:07

171

Views

Proving $\exists x[P(x)] \to \exists y[\exists x[P(x)]\to P(y)]$ in for intuitionistic $\varepsilon$-calculus.

Published on 23 Feb 2026 - 12:08

score 60 · Answer 14 · 2026-02-23 12:04:17

60

Views

Making sense of eigenvariable restriction in $\exists L$ rule in sequent calculus

Published on 23 Feb 2026 - 12:04

score 73 · Answer 15 · 2026-02-23 12:04:14

73

Views

Showing if $A[y/x]\models\Delta$ then $\exists x A(x)\models\Delta$

Published on 23 Feb 2026 - 12:04

List Question

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

Proof in Natural Deduction, Sequent Calculus or Hilbert System

Is there a G4ip equivalent for first-order logic?

Reflection principle for finite subsystems of PA.

Establishing $\Gamma, A: Type \vdash (A)Type\ \textbf{kind}$ in LF

Equivalence of Martin-Löf sequent calculus and standard sequent calculus with material implications

Sequents in which succedents are restricted to one formula

Is there some variant of sequent calculus that allows for non-trivial axioms?

Exchange case in proving interpolation theorem by induction on the length of proof tree

What is the correct way to interpret the Intuitionistic rules of Kleene's sequent (Gentzen) system G1 (in sec. 77 of Kleene I.M. 1952)

What is the metatheory required for proving the cut-elimination theorem for classical logic? Is the proof circular?

Understanding quantifier rules in sequent calculus

Proving $\exists x[P(x)] \to \exists y[\exists x[P(x)]\to P(y)]$ in for intuitionistic $\varepsilon$-calculus.

Making sense of eigenvariable restriction in $\exists L$ rule in sequent calculus

Showing if $A[y/x]\models\Delta$ then $\exists x A(x)\models\Delta$

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