Open Logic Project
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Free, open-source collection of logic textbooks maintained by logicians, including Sets, Logic, Computation and Incompleteness and Computability. Covers propositional and first-order logic, natural deduction, completeness, computability and incompleteness, so readers can work through formal proof systems and metatheory rigorously.
More resources on Formal Systems
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
plato.stanford.edu
The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics.
nLab: Formal System
nLab entry defining deductive and formal systems as collections of judgments and inference steps, explaining proof trees and effective enumerability, with natural deduction, sequent calculus, Hilbert systems and type theory as examples. Readers gain a precise, general vocabulary for comparing proof systems.
Stanford Encyclopedia of Philosophy: Proof Theory
Stanford Encyclopedia of Philosophy survey of proof theory: Hilbert's program, axiomatic systems, natural deduction and sequent calculus, cut elimination, Gentzen's consistency proof and ordinal analysis. Readers gain a historical and technical map of how formal proofs are studied as mathematical objects.
Introduction to Logic
Learn the fundamentals of logic and formal systems with this introductory course. Explore reasoning principles and problem-solving techniques.
Logic and Structure
Upper-undergraduate logic textbook by Dirk van Dalen covering propositional and predicate logic via natural deduction, completeness and compactness, basic model theory and intuitionistic logic. Readers learn to prove metatheorems about formal systems rather than simply use them.