# Tag: Wau

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- What is wrong with this in the framework of mathematical logic? June 15, 2024Lets say ~ A ⇒ [ A ∨ ( T ⇒ R) ] ~ R ⇒ [R ∨ (A ⇒ R) ] ( T ∨ D) ⇒ ~ R T ∨ D / D Now solving it. ~ A ⇒ [ A ∨ ( T ⇒ R) ] ~ R ⇒ [ R ∨ (A […]ilikebread
- Why can't three-valued logic (ternary logic) simply have only two truth values? June 15, 2024Consider the statement: P ∧ ¬P ⊢ Q where: P is any proposition, ¬P is the negation of P. Q is another proposition. Wouldn't proving both P and ¬P to be true simply lead to a new proposition Q, rather than introducing a third truth value? Even if we follow the principle of explosion, wouldn't […]Sam
- A generalized algorithm to convert a formula in algebraic normal form to an equivalent formula that minimizes the number of bitwise operations June 15, 2024In this question, “bitwise operation” means any operation from the set {XOR, AND, OR}. The NOT operation is not included because it can be represented as a single XOR with 1. Given an arbitrary formula $f$ (in algebraic normal form), how to find an equivalent formula $g$ that minimizes the number of bitwise operations? For […]lyrically wicked
- How to formalize unary intersection operator? June 14, 2024How can we formalize the $\cap$ (unary intersection) operator? Following is my attempt. I define/construct the function $~\cap : P(P(U)) \to P(U)$ such that: $\forall a\in P(P(U)): \forall b\in U: [b\in \cap a \iff \forall c\in a:b\in c]$ where $U$ is the underlying set being considered, and $P$ is the powerset operator. $P(P(U))$ can be […]Dan Christensen
- the difference of explicit and implicit definition of functions logically June 13, 2024The fundamental analysis book I'm reading has a section on the difference between the implicit and explicit definitions of functions. The implicit definition of a function f specifies what property $ P(x,y) $ links the input x with the output $f(x)$. How is the implicit definition different from an explicit one, showing how one generates […]roro
- Difference of ≡ and ⇔ [duplicate] June 13, 2024I'm studying cs in germany, I have been going through my script starting with propositional logic. I don't really understand the difference between those. I watched some YT-Videos on the topic but i didn't really helped me differentiate between those. They just sometimes use one or the other. "Definition" in my own words (my understanding): […]user1335232
- Morley Rank of disjunction is equal to the maximum of the Morley Rank of the disjuncts June 13, 2024I want to prove that if $X_1, X_2$ are definable subsets (in some suitable theory), then the Morley rank $$\text{MR}(X_1 \cup X_2) = \max(\text{MR(}X_1), \text{MR}(X_2))$$ where MR(-) denotes the Morley rank. This is in Marker's Model Theory (Lemma 6.2.7 ii). I'm trying to prove this by induction and it seems clear to me that this […]XavierbutwithaJ
- What statement is true for every $a$, $b$ and $c$? June 13, 2024I have this task in mathematical logic for which I don't really have a tool for solving. What statement is true for every a, b and c? $a \in b \wedge b \in c \rightarrow a \in c$ $a \in b \wedge b \subseteq c \rightarrow a \in c$ $a \subseteq b \wedge b \in […]Danilo Jonić
- Ramsey's Theorem and Weihrauch reducibility June 13, 2024Let $\text{RT}^n_k$ denote (infinite) Ramsey's theorem for $n$-tuples and $k$ colors. Let $\leq_W$ denote Weihrauch (i.e., uniform) reducibility. It is known that, for fixed $k \geq 2$, if $n > m \geq 2$, then $\text{RT}^m_k \lneq_W \text{RT}^n_k$ (pages 5 and 6 of this paper). It is also known that, for fixed $n \geq 2$, if […]Gavin Dooley
- Defining relations. June 13, 2024Do these answers provide what is required? Even(x)=∃k(x=2*k) Triple(y,x)=∃x(y=3*x)Lior

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