Hi everyone,

The Fall 2018 Calendar for this course has been updated – the final version is now available on the Calendar page.

Regards,

Prof. Reitz

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Hi everyone,

The Fall 2018 Calendar for this course has been updated – the final version is now available on the Calendar page.

Regards,

Prof. Reitz

- OpenLab #1: Advice from the Past – 2019 Fall – MAT 2071 Proofs and Logic – Reitz on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #3: “Sentences”
- Franklin Ajisogun on OpenLab #6: Proof Journal
- Jessie Coriolan on OpenLab #7: Advice for the Future

- Prove logical consequence if and only if A is valid and B is unsatisfiable November 27, 2022Given three formulas $(1) \phi_1:\exists x :p(x)$ $(2)\phi_2: (\forall x : p(x) \Rightarrow q(x))$ $(3) \phi_3: \exists x : q(x)$ Now I need to prove that $\phi_3$ is a logical consequence of $\phi_1 \wedge \phi_2$ if and only if A is valid and B is unsatisfiable. I need to find formulas $A,B$ that each contain […]illuminatitruthseeker
- How is Zorn's lemma proven in ZF(C), actually? November 27, 2022I want to prove some results like that every vector space has a base without the use of Zorn's lemma becuase I want to practice set theory and become confident with things like ordinals. I have some basic understanding of ordinals that I could find online and, if I didn't miss anything, online sources don't […]donaastor
- Does proving that $\pi$ is a parsing tree suffice to say that $\phi$, its associated formula is a formula? November 27, 2022Let $\phi$ be an expression of $LP(\sigma)$, $\pi$ its "parsing" (planar?) tree. If we show that $\pi$, indeed, is a proper parsing tree, that is verify that all of the defining properties hold: $(a)$ Every node has arity $\leq$ 2. $(b)$ Every node of arity 0 (leaf) is an atomic formula in $\sigma$ or $\perp$. […]Maab Student Chaoui
- In logic is it valid to say that Δ ⊢ a is equivalent to Δ → a? November 26, 2022I am new to logic so I'm trying to understand the relationship between some of the symbols and concepts. I am specifically trying to understand the turnstile character, or 'proves' concept. If something proves something else, then is it true that this is equivalent to saying that if it is true, then something follows? As […]Juel Herbranson
- Are these two conditions always equivalent for the lattice $\mathbb Z^d$ for any property (P)? November 26, 2022Consider the lattice $\mathbb Z^d$ in $\mathbb R^d$ and the following two statements: Let $(P)$ be a property on vectors in $\mathbb R^d$ and let $1\le k \le d$. (1) For any $k$ linearly independent vectors $v_1, ... , v_k$ in $\mathbb Z^d$, there exists $v_i$ ($1 \le i \le k$) satisfying the property (P). […]taylor
- Predicate logic tree development November 26, 2022I was wondering how to distinguish between developing predicate logic with (∀x) and (∃x) to forms such as Fa or Fb. What rules tells us an argument or conclusion should be developed with an a or b objet ? For example, here is the development of a tree where Gb is used instead of Ga […]Finn
- Is there any introductory analysis ( or real analysis) book written in symbolic logic? [closed] November 25, 2022I have noticed that well-known books (like Principles of Mathematical Analysis (Rudin) or Understanding Analysis (Abbott)) don't use directly symbolic logic. As far as I know, symbolic logic used to avoid misunderstandings of the theorems. So I have tried to find analysis books written in symbolic logic but I couldn't. So, Do you have any […]mhkn
- Hils-Loeser Ex. 3.3.4: $T'$ is an expansion by definition of $T$ iff every $\scr L$-model of $T$ extends uniquely to a $\scr L'$-model of $T'$ November 25, 2022The textbook is Hils-Loeser "A First Journey Through Logic". Exercise 3.3.4. Let $T\subseteq T'$ be theories in languages $\scr L$ and $\scr L' \supseteq \scr L$, respectively. Prove that $T'$ is equivalent to an expansion by definition of $T$ if and only if every model of 𝑇 admits a unique expansion to a model of […]D.R.
- Reductio ad absurdum when there are no premises and just a supposition $S$ November 25, 2022I was reading An Introduction to Formal Logic by Peter Smith - https://www.logicmatters.net/resources/pdfs/IFL2_LM.pdf , and on page 36 he explains Reductio ad absurdum as: If $A_1, A_2, \dots, A_n$ (as background premisses) plus the temporary supposition $S$ entail a contradiction, then $A_1, A_2, \dots, A_n$ by themselves entail $not$-$S$ He "proves" this by showing that […]Jamāl
- Proof and Demonstration November 25, 2022I started a mathematical logic course this term, and as I understood the first order language can be seen as a tool to do mathematics in a rigorous way. For instance mathematical logic gives us a precise definition of what a proof is, i.e. how to build sequences from others. So, if I start with […]Tom

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