**Written work** – None.

**WeBWorK **– Assignment #5, due Tuesday, October 10th, at midnight.

**OpenLab **– OpenLab #5, due Thursday, October 12th, **before**** class**.

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### Logic on Math StackExchange

- Determining truth values September 18, 2024I know this might sound extremely basic, but I'm currently in discrete math and we are learning logic. I'm actually having a really hard time with questions that ask me to determine the truth value of certain expressions. The one in particular is the following:$$x = 2^4.$$ Apparently this is not a statement, but I'm […]Oldmathdude
- I’m trying to understand how to calculate this proof. [closed] September 18, 2024Im am trying to understand how to solve this proof and my professor said that we cannot use repetition $P \vdash P$.Mikayla Ruff
- The necessary condition in the implication "$p\Rightarrow q$" [duplicate] September 18, 2024My understanding is that in the implication $$p {\implies} q,$$ $p$ is sufficient to conclude $q$, and $q$ is necessary condition for $p$. Let $p$ be "it is raining," and $q$ be "the sidewalk is wet." The sufficient condition statement "If it is raining then it is sufficient to conclude that the sidewalk is wet" […]novice programmer
- Are there consequences to assuming that there are only a certain class of inductively defined functions on any given set? September 17, 2024On any set $X$, it seems intuitive that the only functions $X^n \to X$ we can actually specify are those which follow structurally from, say, the axioms of ZFC. In particular, it seems highly intuitive that this class of functions that can actually be written down is some near-inductively defined set of functions such as […]William Oliver
- Conditional or biconditional for 'except'? September 17, 2024The following translation is given in (part (c) of Q1 of Exercise 2.1 in) the book How to Prove It by Daniel Velleman: Everyone likes Mary, except Mary herself. $$\forall x(\neg(x=m)\rightarrow L(x, m)),$$ where $L(x, y)$ stands for "$x$ likes $y$" and $m$ for "Mary". Acording to this formalisation, $L(m, m)$ is possible. But, according […]Muhammad Safiullah
- Is second-order arithmetic subject to Gödel's first incompleteness theorem? If so, why is it? September 17, 2024I have studied Gödel's first incompleteness theorem for first-order logic (FOL) and believe I grasp the proof. The theorem implies the existence of non-standard models for Peano arithmetic. I also heard that second-order arithmetic is categorical, meaning that all its models are isomorphic. My question is: Is second-order arithmetic subject to Gödel's first incompleteness theorem? […]Victor
- Is “reduct” just another word for “image through a forgetful functor”? September 17, 2024I have just started learning Mathematical Logic in greater depth and I was assigned some lecture notes to read. I noticed how the lecturer often used the word reduct, to mean… a structure which has gone through a transformation, I guess. I’ll give you one example: he had just finished introducing Gödel Algebras, and in […]Melanzio
- Why does the following test for protoalgebracity work? September 16, 2024The following text appears in Janusz Czelakowski's "Protoalgebraic Logics": Suppose there exists a class $\mathbf{K}$ of matrices for a language $S$ and a $k$-parameterized set $E(p,q,\underline{r})$ of sentence in $S$ such that for every matrix $M=(A, D)$ of $\mathbf{K}$ and every pair $a,b\in A$, (a) $E(a, a, \underline{c})\subseteq D$ for all strings $\underline{c}\in A^k$; (b) […]Somebody
- Is Gödel reducible to Cantor? September 15, 2024I have worked out a putative proof of Gödel's Incompleteness Theorem, that is shorter and more to the point; because it moves the assumption of completeness earlier. Is this proof known ? [Mind you it does not assume soundness; if you think the post is incomplete, please be specific because I no longer know what […]Constantine Frangakis
- Turing Machine to Generate the Sequence 10110111011110... of increasing number of symbols September 15, 2024Designing a Turing Machine to Generate the Sequence 10110111011110... on a Blank Tape Question: I am working on designing a Turing machine that, when given a blank tape, generates the sequence 10110111011110..., where the pattern involves increasing the number of 1s between each 0. Specifically, the desired output sequence starts with 1, followed by 0, […]Antonio Guzmán Bucio

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