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mathematical-logic-expert skill

/skills/mathematics/mathematical-logic-expert

This skill analyzes formal logic problems and applies rigorous methods to improve reasoning accuracy across theory, model theory, and computability.

npx playbooks add skill sandraschi/advanced-memory-mcp --skill mathematical-logic-expert

Review the files below or copy the command above to add this skill to your agents.

Files (6)
SKILL.md
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---
name: mathematical-logic-expert
description: Expert in formal logic, model theory, computability, and foundations of mathematics
license: Proprietary
---

# Mathematical Logic Expert
> **Status**: ⚠️ Legacy template awaiting research upgrade
> **Last validated**: 2025-11-08
> **Confidence**: 🔴 Low — Legacy template awaiting research upgrade

## How to use this skill
1. Start with [modules/research-checklist.md](modules/research-checklist.md) and capture up-to-date sources.
2. Review [modules/known-gaps.md](modules/known-gaps.md) and resolve outstanding items.
3. Load topic-specific modules from [_toc.md](_toc.md) only after verification.
4. Update metadata when confidence improves.

## Module overview
- [Core guidance](modules/core-guidance.md) — legacy instructions preserved for review
- [Known gaps](modules/known-gaps.md) — validation tasks and open questions
- [Research checklist](modules/research-checklist.md) — mandatory workflow for freshness

## Research status
- Fresh web research pending (conversion captured on 2025-11-08).
- Document all new sources inside `the Source Log` and the research checklist.
- Do not rely on this skill until confidence is upgraded to `medium` or `high`.

Overview

This skill is an expert agent for formal logic, model theory, computability, and foundations of mathematics. It provides structured guidance, proof intuition, and research-oriented checks for foundational topics. Note: the content is a legacy template that requires fresh literature validation before high-confidence use.

How this skill works

The skill inspects logical definitions, formal proofs, and model-theoretic constructions and highlights gaps or assumptions. It runs a research checklist to collect up-to-date sources and tracks unresolved validation tasks. It also offers step-by-step strategies for formalizing problems, identifying computability boundaries, and evaluating foundational claims.

When to use it

  • Designing or checking formal proofs in first-order logic, set theory, or arithmetic.
  • Evaluating model-theoretic constructions (ultraproducts, saturation, elementary embeddings).
  • Assessing decidability, reducibility, or complexity in computability theory.
  • Preparing research notes, literature reviews, or replication checks for foundational claims.
  • Prior to publishing or presenting results that rely on subtle metamathematical assumptions.

Best practices

  • Run the research checklist and record all sources before trusting technical conclusions.
  • Explicitly document definitions, axioms, and intended semantics for each proof or model.
  • Use the known-gaps list to track open validation items and unresolved lemmas.
  • Prefer small, testable lemmas when formalizing long proofs to catch hidden assumptions early.
  • Flag results as low-confidence until independent sources or formal verification confirm them.

Example use cases

  • Convert an informal argument about completeness or compactness into a formal, checkable proof sketch.
  • Audit a proposed independence result by listing necessary models and verifying forcing or inner-model steps.
  • Determine whether a decision problem is decidable or complete for a known class, and produce a reduction outline.
  • Prepare a literature-backed summary of current gaps in a subfield (e.g., computable model theory) before a grant proposal.
  • Generate a stepwise plan to formalize a paper’s central proof for mechanized verification.

FAQ

Is the skill ready for definitive technical claims?

No. The skill is based on a legacy template and should be used only for drafting, checking intuition, and preparing research tasks until sources have been refreshed and confidence upgraded.

How do I improve confidence in results produced by the skill?

Run the research checklist to gather primary sources, resolve items from the known-gaps list, and, where possible, cross-check proofs against independent references or a proof assistant.