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A Kurepa tree is called an essential Kurepa tree if it contains no Jech--Kunen subtrees. A Jech--Kunen tree is called an essential Jech--Kunen tree if it contains no Kurepa subtrees. In this paper we prove that (1) it is consistent with CH and 2^{omega_1}> omega_2 that there exist esse"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9401217","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1994-01-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"42b18a219563f9e2459b1d4e6d5a93e5fcc2f280a8cfa373ff1336cbe5aee284","abstract_canon_sha256":"7a178aa4e96045213b34febef1ae221769196b1aec98a94759d6bc3453025f3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.705215Z","signature_b64":"W4dwWQ6TPQ/LkdjV6UiTtK0lJ7aEukUogwSBpBjB6N5DuIpFXIvM73Kf10XZJbKdT61Mzn74ou1wAIta/K6uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5268fc18b46ff750cd231e35fab72f102f245729f55564b9dde030c945db9c31","last_reissued_at":"2026-05-18T01:05:51.704785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.704785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Essential Kurepa trees versus essential Jech---Kunen trees","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Renling Jin, Saharon Shelah","submitted_at":"1994-01-15T00:00:00Z","abstract_excerpt":"By an omega_1 --tree we mean a tree of size omega_1 and height omega_1. 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