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Dear All,

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Sep
23
comment Induction, how often?
I have constructed the example from the property that ∀x doesn't preserve countable infinite ascending unions. The existential quantifier does so. But I am not yet sure what the implications are for induction. Maybe one can construct a predicate q, prove it by a single induction, and then derive p. Like following the odd numbers and hypothetically following the even numbers at the same time, and joining the two together resolving the hypothesis. The hypothesis would be p(1).
Sep
23
revised Induction, how often?
added 43 characters in body
Sep
23
comment Induction, how often?
Greetings from CH to CH. Looks like an agreement that ∀x p(x) holds. But somehow the proof doesn't go through with a single induction over p, does it?
Sep
23
revised Induction, how often?
deleted 1 characters in body
Sep
23
asked Induction, how often?
Sep
22
comment Why does the expression of Peano induction has to be second order?
Actually first order induction means that one adds a schema. So the X is really quantified, but not in the object logic but syntactically on the meta-level.
Sep
21
revised What are the historical roots of cryptarithmetic?
added 58 characters in body
Sep
21
answered How to prove AB is not equal to BC
Sep
21
asked What are the historical roots of cryptarithmetic?
Aug
25
revised What kind of logics satisfy the coincidence lemma?
added 286 characters in body; edited title
Aug
22
comment What kind of logics satisfy the coincidence lemma?
Then the truth can depend on more than only p and x. For example if I substitute f(y) for x, and in one case a for y and in another case b for y. I could get different truth values.
Aug
22
comment What kind of logics satisfy the coincidence lemma?
Take p(x). Usually the truth value of the above sentence only depends on the interpretation of p and the domain value of x. But what if we allow to determine the truth to perform simultaneous non-ground substitutions?
Aug
22
comment What kind of logics satisfy the coincidence lemma?
If sigma is not an interpretation, but a simultaneous non-ground substitution, then the lemma doesn't hold. Right? Is there some logic that would amount to that?
Aug
22
awarded  Yearling
Aug
22
comment What kind of logics satisfy the coincidence lemma?
Yeah, possibly we could define occuring free in A after the fact semantically and not before the fact syntactically, by virtue of this lemma.
Aug
22
revised What kind of logics satisfy the coincidence lemma?
edited body
Aug
22
comment logic question: enumerating propositions
How about HOL with some general semantics? Not the full semantic?
Aug
22
asked What kind of logics satisfy the coincidence lemma?
Aug
15
revised Need an asymptotic function that's going to have a specific shape
added 123 characters in body
Aug
15
accepted Epistemic disjunction, axiom or rule?