This University of Oxford Part C paper is cross-listed for Mathematics and Mathematics and Philosophy. Section A concerns Gödel second incompleteness theorem and provability logic; section B concerns model theory. ^[ref] The archive contains the complete editable four-page transcription. Bounded official-source searches found no advertised answers to this exact paper. All 31 source leaves are answered below. The enumeration and function-definability conventions are stated explicitly, and the canonical-model construction uses the function-free setting permitted by the source.

This University of Oxford Part C paper is cross-listed for Mathematics and Mathematics and Philosophy. Section A concerns Gödel second incompleteness theorem and provability logic; section B concerns model theory. ^[ref] The archive contains a complete editable six-page transcription. Bounded official-source searches found no advertised solutions to this exact paper. All 37 source leaves are answered below. The solutions state the proof-numbering convention in A2(d), the naming convention for diagram inclusions in B6(ii), and the literal printed stability definition in B8(ii)(e).

This University of Oxford Part C paper covers Gödel's Incompleteness Theorems in section A and Model theory in section B, cross-listed for Mathematics, Mathematics and Computer Science, and Mathematics and Philosophy. ^[ref] The archive contains the complete editable five-page transcription. Bounded official-source searches found no advertised answers for this exact paper. A2(c) is answered with a counterexample to its literal semantic hypothesis and a proof of the intended canonical case. The vector-space comparison keeps infinitude of the underlying set distinct from infinite dimension.

Source release: Oxford examination archive release thread, Part C bundle pages 300–304. This is one combined paper covering both courses: section A concerns Gödel second incompleteness theorem and provability logic, and section B concerns model theory. The cover cross-lists Mathematics and Mathematics and Philosophy, both Part C, Thursday 10 June 2010, 2.30pm–5.30pm.

Answer availability checked on 28 October 2026: bounded official Oxford searches by exact year, paper label and both subjects found no advertised exact-paper answers. The official Part C syllabus for the 2010 examination confirms the paired course identity. No later-year answer-release policy was assumed applicable.

Source paper: Mathematics Part A FOI release, member FOI-20210708-1 - Data/4321.pdf. The original cover identifies Metric Spaces and Complex Analysis, A2, formal code 4321, Friday 20 June 2014, 9.30am to 12.30pm. All four source pages are readable.

Original sitting: Friday 19 June 2015, 9.30am to 12.30pm. The recovered original cover establishes this date despite the enclosing archive's directory label. ^[ref]

The complete five-page replacement is in the Mathematics Part A FOI release, member FOI-20210708-1 - Data/a13754w1 (3).pdf. Its intact printed page 2 supplies Questions 1–3; the readable original Questions 4–6 and all twelve existing answers are retained unchanged. The original archive link above is preserved for provenance.

Source paper: released examination archive, member 2015/T/a13754w1.pdf. The cover dates this paper to 2016-06-14.

Solutions already advertised by Oxford. The Mathematical Institute releases examination solutions for even-numbered years dating back to at least 2016; this paper is skipped here. ^[ref]

A complete readable copy is now held from the Mathematics release, member FOI-20210708-1 - Data/a13754w1 (2).pdf. The local examination archive contains a complete transcription; the advertised-solution policy above still applies.

Source paper: released examination archive, member 2016/T/a13754w1.pdf. The printed cover dates the examination to 13 June 2017. All six questions and all thirty-four terminal subparts are answered below, including the definitions and other requirements printed outside the nested lists.

This University of Oxford Part C paper combines Methods of Functional Analysis for PDEs in section A with Fixed point Methods for Nonlinear PDEs in section B. ^[ref] The archive preserves the full editable seven-page paper. Bounded official-source searches found no advertised answers for this exact paper. Question 3 has a missing spectral term in one printed adjoint weak-form assertion; the solution gives a counterexample and the corrected derivation.

Original solutions to both sections, all six questions and all twenty-five terminal parts of the Methods of Applied Functional Analysis paper sat on 8 June 2010. Source: released Mathematics papers, Part C 2007 11.pdf.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Open the original paper in the scanned volume, PDF pages 93–93.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

The historical discussions reconstruct defensible reasoning available in December 1867; they are not an official answer key. Each is followed by a present-day correction where the underlying theory or treatment has changed. Clinical descriptions below are hypothetical teaching patterns, not records of actual patients. Historical quantities describe historical practice and are not current prescriptions.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Original scanned volume, PDF page 99. Oxford, December 1867.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

The answers distinguish the terminology and therapeutic possibilities of 1867 from present medicine. They explain general anatomy, physiology and clinical reasoning; no individual patient or examination findings are assumed.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Open the original paper in the scanned volume. Source range: PDF pages 91–91.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

These historical-exam solutions distinguish terminology current in 1867 from present-day pathology. Modern mechanisms and tests are identified as such; the paper supplies no individual patient records or specimens.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Open the original paper in the scanned volume, PDF page 89.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

The historical standard used below is the British Pharmacopoeia by the General Medical Council (1867). A contemporary July publication notice records official publication notices dated 14 June 1867, before this December examination. Later reprints containing the additions of 1874 must be distinguished from this original issue.^[ref] These are explanations of historical materia medica, with present physiology identified separately where it changes the interpretation.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867), scanned PDF page 95. Open the original paper in the scanned volume.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Open the original paper in the scanned volume.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). The paper occupies PDF volume pages 101–102 (Oxford, December 1867, No. VII.). Open the original paper in the scanned volume.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Open the original paper in the scanned volume, PDF page 81.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.

Original volume: Examination papers for the Degree of Bachelor of Medicine by the University of Oxford (1864–1867). Original paper, PDF pages 85–86.

Original questions are transcribed from the public-domain edition. Credit: Wellcome Collection; original supplied by Royal College of Physicians, London. Source and public-domain rights statement.