Questions tagged [second-order-logic]

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Prove that the prime numbers set can be defined in a model

Given first order language, $L = <0, S, +, \cdot, = >$, $0$ is the number zero, $S$ is the successor function, and a model $M$ with the domain $\mathbb{N}$, I need to prove that the prime ...
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Can we get something equivalent to $\mathsf{ZFC2}$ by naively allowing the separation and replacement to range over second-order wffs? [duplicate]

I've seen $\mathsf{ZFC2}$ mentioned in a few questions such as this one and I'm curious about ways to axiomatize it that have the fewest differences from plain $\mathsf{ZFC}$ as possible. My question ...
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Expressing "finitely many", "infinitely many", "most" and "more" in second-order logic

Famously it is impossible to express "finitely many" or "most" and so on in first-order logic, but we can apparently do so in second-order logic. Unfortunately, I cannot find ...
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Suggestions for learning natural deductions in simple and ramified second order logic

I am reading the book Natural Deductions: A proof-theoretic study by Dag Prawitz and stuck at the chapter V of this book, which is about natural deduction in second order logic. Before reading this ...
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Why second order logic is more expressive that the first order logic?

As far as I understand, the second order logic is more expressive than the first order logic because it can make statements about predicates. However, I do not understand why this problem (...
• 453
Let $\mathcal L_Q$ be the logical system that includes first order logic together with the quantifier $Q$ which is defined as follows: For an interpretation \$\mathfrak I=(\mathfrak A, \beta)=((A,\...