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Oct
9
awarded  Critic
Oct
9
comment Confused about Wikipedia definition of NP
"Efficient" always means "verifiable in polynomial time in the length of the input". And in this case the input is the formula, not the ZFC-proof.
Oct
9
comment Confused about Wikipedia definition of NP
In the Wikipedia there is no formal definition since the term used is "efficiently verifiable". Do you guess how to translate this expression to a formal setting?
Aug
26
comment Proper classes and models of set theory
$V_k$ is a set (for all $k$), not a proper class. Thus, I do not see the connection with your question.
Aug
26
comment Proper classes and models of set theory
A class is just a formula with one free variable. Some formulas define sets, and the ones that do not define sets are called proper classes. Hence, think about your question when you consider the formula "$x=x$"; does it define a set or always a proper class?
Aug
9
comment Undecidability in ZFC of statements concerning logical validity
Very nice (and simple) way to answer the question. Finally, I have chosen Carl's answer because it produces an example of such formula.
Aug
9
accepted Undecidability in ZFC of statements concerning logical validity
Aug
9
comment Undecidability in ZFC of statements concerning logical validity
@Carl: Could you give some hint on what you mean by Morse-Kelley set theory? In its Wikipedia page it is said that "Morse–Kelley set theory cannot be finitely axiomatized", so it is not clear to me what formula is $\psi$.
Aug
9
comment Undecidability in ZFC of statements concerning logical validity
@Carl: Thanks for replying Asaf (your convention is the same one I use).
Aug
9
revised Undecidability in ZFC of statements concerning logical validity
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Aug
9
revised Undecidability in ZFC of statements concerning logical validity
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Aug
9
revised Undecidability in ZFC of statements concerning logical validity
added 3 characters in body
Aug
9
asked Undecidability in ZFC of statements concerning logical validity
Jul
19
answered Mathematician (non-logician) seeks reference for Gödel's incompleteness theorems
Jul
1
accepted About the pointwise infimum of a continuous piecewise linear function
Jul
1
comment About the pointwise infimum of a continuous piecewise linear function
OK I see. Thus, the natural generalization to the rational setting (see the last part of my question) is whether it is true or false that every finite set of rational points can be "rationally triangulated". Any suggestion for a book where I can find similar statements (and a proof of the triangulation theorem)?
Jul
1
comment About the pointwise infimum of a continuous piecewise linear function
Thanks for the answer. Which "triangulation result" are you using here?
Jun
30
revised About the pointwise infimum of a continuous piecewise linear function
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Jun
30
comment About the pointwise infimum of a continuous piecewise linear function
Yes, there are finitely many pieces (and each one of them can be thought as the convex hull of a finite set of points)
Jun
30
asked About the pointwise infimum of a continuous piecewise linear function