Hi everyone,

Attached are the final drafts of each group paper – excellent work, everyone!

Best regards,

Prof. Reitz

ismael_jeron_hanan_proofs-and-logic-group-paper

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Hi everyone,

Attached are the final drafts of each group paper – excellent work, everyone!

Best regards,

Prof. Reitz

ismael_jeron_hanan_proofs-and-logic-group-paper

- A doctrine is a categorification of a theory September 28, 2023So it says in the nlab page of doctrine. Let's focus on first order theories for simplicity. I have two questions, one regarding vertical categorification and another regarding horizontal categorification. My final goal would be to understand first order hyperdoctrines as a vertical categorification of first order theories with possibly some extra conditions. First I […]Julián
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- I believe in another logic where there is no Gödel incompleteness theorem [closed] September 28, 2023In my logic, a sentence can be true, false, or meaningless. An example of meaningless sentence would be liar paradox. Now assume there is a theory T which formalizes the classical arithmetic. For sure, you can construct a Godël sentence but its interpretation is not the same, it now says : You can construct a […]François
- Confusion on Basic Logic Question about Contrapositive (simple probably) September 28, 2023So, suppose we are told to show the statement: "If $\frac{1}{x}$ is irrational, then $x$ is also irrational." This seems pretty clearly true, and I can't think of a counterexample, but when we consider the logically equivalent contrapositive: "If $x$ is rational, then $\frac{1}{x}$ is rational." we see that this statement is untrue for $x=0$. […]Unknown
- Is there a modal operator, L, that satisfies φ ↔ 𝛙 & ~L𝛙 ⊢ ~Lφ? September 28, 2023I am wondering if there's some modal operator that would satisfy $$φ ↔ 𝛙 \& ~L𝛙 ⊢ ~Lφ.$$ That is: Given $φ ↔ 𝛙 \& ~L𝛙$ You can get to $~Lφ$ One limitation is that $L$ for sure does not satisfy modal axiom $T$: i.e., it's not the case that if $Lφ → φ$. Otherwise, […]Melody
- Transform to CNF (conjunctive normal form) September 27, 2023I am trying to convert the following expression to CNF (conjunctive normal form): $\left(A\Rightarrow B\right)\Rightarrow\left(A\Rightarrow C\right)$ As my first steps I am removing the implications like so: $\left(\lnot A ∨ B\right)\Rightarrow\left(\lnot A ∨ C\right)$ $\lnot\left(\lnot A ∨ B\right)∨\left(\lnot A ∨ C\right)$ Removing the negation by applying it to the parentheses: $\left(A\land\lnot B\right)\vee\left(\lnot A\vee C\right)$ Until […]Student17
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- Is "non-rigid" first-order axiomatisable? September 27, 2023As I've recently been genning up on some of my undergraduate courses, I took a passing interest in the Part II Cambridge Maths Tripos questions from the exams sat earlier this year. One question, from the Logic and Set Theory course (p63 at the above link), that caught my eye was the following: If a […]jst345
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- How should one understand the "universe of sets"? September 27, 2023One way to understand the axioms of $\mathsf{ZFC}$ is to see them as a describing the "universe of sets" $V$, together with the "true membership relation" $\in$. The universe $V$ is built up in stages: \begin{align} V_0 &= \varnothing \\[4pt] V_{\beta+1} &= \mathcal P(V_{\beta})\quad\text{for every ordinal $\beta$,}\\[4pt] V_{\lambda}&=\bigcup_{\betaJoe

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