A Model Theory for the Potential Infinite

We present the model theoretic concepts that allow mathematics to be developed with notion of potential infinite instead actual infinite. The is understood as a dynamic notion, being an indefinitely extensible finite. main adoption interpretation universal quantifier, which has implicit reflection principle. Each quantification refers large, but finite set. quantified sets may increase, so after reference by quantification, further typically uses larger, still for classical first-order logic and show these models are sound complete respect usual inference rules. Moreover, set formulas requires part increasing correct interpretation.