Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill logic-set-theory-foundationsgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/logic-set-theory-foundations)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/logic-set-theory-foundations"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/logic-set-theory-foundations/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/logic-set-theory-foundations"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/logic-set-theory-foundations.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00075 | $0.00554 |
| Opus 5.5 | $0.00030 | $0.00222 |
| Sonnet 5.5 | $0.00015 | $0.00111 |
| Haiku 4.5 | $0.00007 | $0.00055 |
Grade A, and why
logic-set-theory-foundations scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 29 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Logic, Set Theory & Foundations
Logic
- Propositional: connectives, truth tables, equivalences (De Morgan, contrapositive), normal forms (CNF/DNF), SAT, resolution, completeness theorem.
- Predicate logic: quantifiers, negating (not forall = exists not), free vs bound variables; models, satisfiability, Goedel completeness, compactness, Lowenheim-Skolem.
- Proof techniques: direct, contrapositive, contradiction, induction (weak, strong, structural), well-ordering, pigeonhole, cases, constructive vs non-constructive, double counting, extremal principle, invariants, probabilistic method.
Set theory
- ZFC axioms: extensionality, pairing, union, power set, infinity, separation, replacement, foundation, choice. Russell's paradox motivates restricted comprehension.
- Cardinality: |N| = aleph_0, |R| = 2^aleph_0 > aleph_0 (Cantor diagonal); Cantor's theorem |P(A)| > |A|; Schroeder-Bernstein; cardinal arithmetic.
- Ordinals and transfinite induction; well-ordering theorem; Zorn's lemma; equivalence of AC with these.
- Continuum hypothesis independent of ZFC (Goedel, Cohen forcing). Large cardinals.
Computability & incompleteness
- Turing machines, Church-Turing thesis, halting problem undecidable, Rice's theorem, decidable vs semi-decidable, lambda calculus, primitive recursive vs recursive functions.
- Goedel's incompleteness: any consistent, effectively axiomatized theory containing arithmetic is incomplete and cannot prove its own consistency. Tarski undefinability, Chaitin's Omega, Kolmogorov complexity.
- Complexity theory classes P, NP, PSPACE, EXP, BPP, BQP; oracle/diagonal arguments.
Alternative foundations
Type theory (Curry-Howard: proofs as programs), category theory, homotopy type theory, intuitionistic logic, proof assistants (Lean, Coq, Isabelle) and formal verification.
Writing a proof
State claim precisely, list assumptions, structure the argument (base case/inductive step), cite lemmas, end with the conclusion, and double-check edge cases.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 29 lines · 75 tokens per session scan A cea1372a4149
logic-set-theory-foundations is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 75 tokens to every session and 554 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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