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

- Is the "set" of all well-founded sets not well-founded? Question about Mirimanoff paradox. September 13, 2024First, let me state the definition of well-founded set that I work with: a set $X$ is well-founded if there is no infinite sequence $\langle x_0, x_1, x_2,\dots\rangle$ of members of $X$ s.t. $x_0\ni x_1\ni x_2\ni\dots$ Now to the question: there is a less known paradox of naive set theory which concerns the concept of […]kevin.spacey
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- The meaning of an implication in an existential quantifier September 13, 2024My professor answered my question on a class discussion board for Discrete Math, but it seems like his answer is just not correct. Could another person who is familiar with this topic weigh in? For context, the function $C(x)$ means that $x$ is a comedian, and $F(x)$ means that $x$ is funny. My Question: Example […]Edward45
- Math logic and proof [closed] September 12, 2024Why does the duty of proof/refutation in mathematics lie with the disprover rather than the assertor? In all the humanities, the opposite rule applies. In other words, to disprove the presence of Russell's teapot in the Earth's orbit from the point of view of mathematical logic, it is necessary to fly the whole orbit and […]Никита Теленков
- Do any recursive field extensions of this field not have a recursive sequence of increasing degree? September 12, 2024Let $F$ be the field $\mathbb{Q}(\{\sqrt{p_n}:n\in K\})$ where $K$ is the halting set and $p_n$ is the $n^{th}$ prime number. $F$ is the standard example of a recursive field without a splitting algorithm. My question is, does there exist a recursive field $E$ which is an infinite algebraic extension of $F$ such that there exists […]Keshav Srinivasan
- Is it not possible to model injective functions using propositional logic? September 12, 2024I'm having some trouble with this question from the 2024 Cambridge Tripos exams: Let $X, Y$ be infinite sets such that there is an injection from $X$ to $Y$. For each $x ∈ X$, let $A_x$ be a non-empty, finite subset of $Y$. Let $P$ be a set consisting of pairwise distinct primitive propositions $p_{x,y}$ […]jst345
- why omega+1 different 1+omega? [duplicate] September 11, 2024I understand that when A is well-ordered, disjoint from {b}, and isomorphic to the ordinal ω (the set of natural numbers), you can construct an isomorphism between the ordinal ω+1 and A⨁{b}. I also understand how you construct the isomorphism by mapping b to 0 and defining f(ak)=k+1 for ak∈A (where k is a natural […]유준상
- Counter example in logics September 11, 2024Studying logics I saw the following problem: If Δ ⊨ α and Γ ∪ {α ∧ β} ⊨ δ, then Γ ∪ Δ ⊨ δ. So, using valuation, I concluded that it is false. But, I need to find a counter example to convince myself. I tried to do the following: Let Δ = {p} […]Carinha logo ali
- Could ZFC be proven consistent for good by some other system that can prove its own consistency? September 11, 2024Is it impossible that Con(ZFC) could be once upon a time proven by a formal system S that is able to prove its own Con(S), i.e. proving Con(ZFC) for good? S would need to avoid Gödel 2, i.e. needing to be weaker than our arithmetic with natural numbers. But that would mean Cn(S) $\subseteq$ Cn(ZFC) […]Pippen
- Mathematical Skepticism [closed] September 11, 2024Let S be an arbitrary formal system. We wanna prove if S is consistent, Con(S), or not, ~Con(S). There are two possibilities only: Some S‘ proves Con(S) but in that case we‘d need to know if Con(S‘) because if ~Con(S‘) then efq and it follows ~Con(S). But so we need S’‘ to prove Con(S’) and […]Pippen

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