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Results tagged with proof-theory
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user 3154
For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.
4
votes
1
answer
871
views
Derivability conditions for Robinson arithmetic
Two pieces of hearsay I have encountered about Robinson's Q:
Q fails to satisfy the Löb derivability conditions;
Pudlák criticised the Löb derivability conditions and suggested rival, weaker conditi …
- 2,283
9
votes
Most general formulation of Gödel's incompleteness theorems
Theories can be be represented recursion-theoretically by an encoding of the language as natural numbers (most simply, a bijective encoding, which I assume), and a Turing machine that accepts all and …
- 2,283
8
votes
Accepted
Reducing ACA₀ proof to First Order PA
Chapter nine of Simpson (1999) Subsystems of Second-Order Arithmetic proves (a) by showing how to construct a second-order model for ACA0 from a first-order model of PA.
(b) The "second-order" we are …
- 2,283
13
votes
What was Gödel's real achievement?
Hilbert, in his 1922 "New Grounding of Mathematics" and subsequent papers, developed an approach to axiomatisation of proof that Goedel's result can be seen to have continued, whilst at the same time …
- 2,283
10
votes
Accepted
What does the disjunction elimination rule say?
The first rule is not the regular disjunction elimination rule, but is known as disjunctive syllogism, and is essentially the modus tollendo ponens rule of term logic. The two rules are mutually admi …
- 2,283
8
votes
Do you know any good introductory resource on sequent calculus?
Gentzen, 1934, 'Investigations into Logical Deduction' — This is very readable, and introduces so many ideas that later synthetic works invariably miss some. If you're serious, this, and some other p …
- 2,283
5
votes
What does it mean to 'discharge assumptions or premises'?
In the spirit of Kenny's observation, note also that we can formulate classical logic using a Peircian inference rule (equivalent to the usual theory in the presence of ex falso quodlibet) which clear …
- 2,283
2
votes
cut elimination
To elaborate on Alexey's answer, for "usual" sequent calculi, the rules other than cut "build structure" in the proof: the left rules build up structure of the assumptions from smaller formulae, and t …
- 2,283