Hi everyone,

The grades for Exam #3 are posted on the “Grades” page – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

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Hi everyone,

The grades for Exam #3 are posted on the “Grades” page – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

- How to prevent ambiguity that arises from conditional statements with multiple conditions or results? August 11, 2024Conditional statements are important when writing mathematical proofs/articles. However, I often need to make conditional statements with multiple conditions/results in the same sentence. Consider this example sentence with multiple conditions: "For any $(a,b,c,d) \in A$, $a=1$ if $b=1$ and $c=1$" This could be interpreted as meaning $(a=1)\textit{ if }(b=1 \land c=1)$ or it could be […]Jonathan
- Does a constant symbol with a free variable imply a contradiction in FOL? August 11, 2024When listening to this talk, I came across an interesting claim (at 12:30) which I wanted to verify: [...] We have defined a constant (called and) which takes no arguments and unfolds to something containing variables $a$ and $b$, which can be whatever we like. It is an interesting exercise to show that a constant […]God bless
- How to prevent ambiguity that arises from multiple conditional statements in one sentence? August 11, 2024Conditional statements are important when writing mathematical proofs/articles. However, I have found that it is sometimes important to be able to have multiple conditional statements in the same sentence when trying to prove something. Consider this example sentence that is dependent on the result of some previous sentence (this is why the sentence starts with […]Jonathan
- Choice of bound in the Laver property August 11, 2024$\newcommand{\P}{\mathbb{P}}$ Recall the following formulation of the Laver property (Page 459, Combinatorial Set Theory: With a Gentle Introduction to Forcing (Second Edition) by Halbeisen): Laver Property. Let $\mathcal{F}$ be the set of all functions $S : \omega \to \operatorname{fin}(\omega)$ such that for every $n < \omega$, $|S(n)| \leq \color{red}{2^n}$. A forcing notion $\P$ has the […]Clement Yung
- Step 2 of Completeness proof in Endertons' "Mathematical Introduction to Logic" August 11, 2024Step 2 of the completeness proof in Enderton's "Mathematical Introduction to Logic" (p. 136) reads: "For each wwf $\phi$ (in the new language) and each variable $x$ we want to add to $\Gamma$ the wff $\neg\forall x\phi \to \phi[c/x]$ where $c$ is one of the new constants symbols. We can do this in such a […]Promethèus
- Introductory modal logic book for mathematicians August 10, 2024I am a mathematician who never had a course in logic, and I'd like to learn about it, especially modal logic and the relationship with topology. Can you recommend me an introductory book? Feel free to ask me any questions that may be relevant to choose the recomendations.user210089
- Implication in one-to-one function definition August 10, 2024Reading Tao´s Analysis, I have seen the following definition of one-to-one functions: I am thinking about something rather simple here: Shouldn´t the implication be an equivalence instead? I thought about the following: We have the statement: $x \neq x´ \rightarrow f(x) \neq f(x´)$. Then we have the four cases for every $x$,$x´$ pair: $x \neq […]Ufuk Can Bicici
- Is there any way to estimate inconsistency probabilty? August 9, 2024Suppose one is given some language $\mathfrak{L}$. Is there any way to estimate the probability that a randomly chosen set of $n$ formulæ (all of length $\leq k$) is inconsistent?Sho
- Abstracting the Undecidability of the Halting Problem August 9, 2024Let us work in some constructive metalogic (where we have at least the following: Natural numbers, Booleans, Lists, Disjoint Union, and Sets). To reason about Turing machines, we could (probably) define the following (metalogical) functions and sets: TMData : Set == Seq(Bool) // TMData is the set of all finite boolean sequences TMEval(alg: TMData, input: […]Suraaj K S
- Are infinite proofs legitimate? August 9, 2024Of course any proof must be, in the most literal sense, finite (must be written down on a finite stack of paper or storage drive of finite capacity). But even on a finite piece of paper one can construct "effectively infinite" statements. For example, suppose I define infinite class of (finite) first-order logic formulas, e.g. […]NikS

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