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Models of PAI are of the form (M, I), where M is a model of PA, I is an unbounded set of order indiscernibles over M, and (M, I) satisfies the extended induction scheme for formulae mentioning I. Our main results are Theorems A and B below.\n  Theorem A. Let M be a nonstandard model of PA of any cardinality. M has an expansion to a model of PAI iff M has an inductive partial satisfaction class.\n  Theorem A yields the following corollary, which provides a new characterization of countable recursively saturated models of PA:\n  ","authors_text":"Ali Enayat","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-12-16T11:25:01Z","title":"Indiscernibles and satisfaction classes in arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.08411","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83e8fc5142a2aec5b34788d2c880d68e1c90181610c697ea252d9a7a182da5ab","target":"record","created_at":"2026-07-05T05:25:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"52f5c83082f99bdd8578756c498ebe59d684b574b1685aa7239d8227275b801c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-12-16T11:25:01Z","title_canon_sha256":"cea3017137391dbdcc2d0e7b02ececd8e5f9f44f9c2eef71f8f2fd3d46eb3ea1"},"schema_version":"1.0","source":{"id":"2212.08411","kind":"arxiv","version":1}},"canonical_sha256":"6a69519675032b04599c6d95223ff9f1f721bcc06ef590cdee8f35374c9b7c64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a69519675032b04599c6d95223ff9f1f721bcc06ef590cdee8f35374c9b7c64","first_computed_at":"2026-07-05T05:25:56.887760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:25:56.887760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/sKl0MyMU4jrdprZJbuezRO248FYQUrQq25i1SNi3bSDE3bbhq17pmvRq9OPtdfcLaW8mROrh7JOV1HhQRs/Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:25:56.888201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.08411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83e8fc5142a2aec5b34788d2c880d68e1c90181610c697ea252d9a7a182da5ab","sha256:77aad7fbdf08cab4d47f42db7a10d18f3c41c04b465cee4305ccbb081d3aaa5f"],"state_sha256":"28f038696898b40ab1fc792f402dc9fdb2dc3bb4a51b12e38009414d0b157861"}