I'm a mathematics professor. My research is in mathematical logic, closely related to computability theory.
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8h
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What are some examples of subtle logical pitfalls? @Asaf: that result is pretty, but it is a standard sort of overspill argument |
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21h
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What are some examples of subtle logical pitfalls? Part of the reason for this confusion, I am sorry to say, is that set theorists are often not very clear about the metatheory/object theory distinction in their writing. (Of course I have some bias about this from working with proof theory.) The confusion with point 1 could be avoided by writing "for every metafinite subset $S$ of the ZFC axioms, ZFC proves that $S$ has a model". |
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1d
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Can the nonexistence of a constructive proof be proven when an existential proof exists? added 365 characters in body |
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1d
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Finite ultraproduct added 768 characters in body |
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1d
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answered | Can the nonexistence of a constructive proof be proven when an existential proof exists? |
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1d
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$f:[a,b]\to\mathbb{R}$ be a measurable function Then which of the following are true? This question lacks two key pieces of information: where did you encounter the question, and what have you already tried? |
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1d
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Riemann integral and Lebesgue integral What does this question have to do with the Riemann integral mentioned in the title? |
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1d
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Riemann integral and Lebesgue integral The question does not have key information: where did you encounter the question, and what have you already tried? |
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2d
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awarded | Nice Answer |
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2d
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Prove that $\int_{-\infty}^{\infty} \sin x \, dx = 0 $ @Dominic Michaelis: as a Lebesgue integral, because the integral of the positive part is infinite and the integral of the negative part is infinite, the overall integral is undefined. $\sin(x)$ is certainly a measurable function on $\mathbb{R}$, because it is continuous. |
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2d
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answered | Finite ultraproduct |
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2d
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answered | What is a proof? |
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May
19 |
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Do all true number thesis with universal form allways has a proof？ The twin primes conjecture is not a universal sentence in arithmetic, it is $\Pi^0_2$. |
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May
19 |
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awarded | Constituent |
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May
19 |
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The consistency of PA is falsifiable. Can the same be said of its soundness? added 1930 characters in body |
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May
19 |
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The consistency of PA is falsifiable. Can the same be said of its soundness? added 2 characters in body |
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May
19 |
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The consistency of PA is falsifiable. Can the same be said of its soundness? @user18921: most theories have intended interpretations, but we treat them just as theories within first-order logic rather than as entirely separate logical systems. The definition of soundness for a logic is not the same as the definition of soundness for a theory, and you want the definition of soundness for a theory. If we take PA + first-order logic to be a separate logic $L$ then this is indeed sound for first-order semantics: a sentence is provable in $L$ if and only if the sentence is true in every structure satisfying the axioms and inference rules of $L$. |
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May
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The consistency of PA is falsifiable. Can the same be said of its soundness? @Michael Greinecker: soundness of a theory means that all of its theorems are true. |
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May
19 |
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The consistency of PA is falsifiable. Can the same be said of its soundness? added 856 characters in body |
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May
19 |
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answered | The consistency of PA is falsifiable. Can the same be said of its soundness? |
