{"paper":{"title":"Back and Forth Systems of Condensations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. Kurili\\'c","submitted_at":"2018-07-01T14:46:15Z","abstract_excerpt":"If $L$ is a relational language, an $L$-structure ${\\mathbb X}$ is condensable to an $L$-structure ${\\mathbb Y}$, we write ${\\mathbb X} \\preccurlyeq _c {\\mathbb Y}$, iff there is a bijective homomorphism (condensation) from ${\\mathbb X}$ onto ${\\mathbb Y}$. We characterize the preorder $\\preccurlyeq _c$, the corresponding equivalence relation of bi-condensability, ${\\mathbb X} \\sim _c {\\mathbb Y}$, and the reversibility of $L$-structures in terms of back and forth systems and the corresponding games. In a similar way we characterize the ${\\mathcal P}_{\\infty \\omega}$-equivalence (which is equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00338","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}