In mathematical logic, geometric logic is an infinitary generalisation of coherent logic, a restriction of first-order logic due to Skolem that is proof-theoretically tractable. Geometric logic is capable of expressing many mathematical theories and has close connections to topos theory.

A theory of first-order logic is geometric if it can be axiomatised using only axioms of the form ${\displaystyle \bigwedge _{i\in I}\phi _{i,1}\vee \dots \vee \phi _{i,n_{i}}\implies \bigvee _{j\in J}\phi _{j,1}\vee \dots \vee \phi _{j,m_{j}}}$ where I and J are disjoint collections of formulae indices that each may be infinite and the formulae φ are either atoms or negations of atoms.^{[citation needed]} If all the axioms are finite (i.e., for each axiom, both I and J are finite), the theory is coherent.

Every first-order theory has a coherent conservative extension.^{[citation needed]}

Dyckhoff & Negri (2015) list eight consequences of the above theorem that explain its significance (omitting footnotes and most references):