Ok - did some lightining research.
s.3 SAF Act:
3. The following persons shall be persons subject to military law and this Act shall, subject to such exclusions or variations in relation to non-uniformed servicemen as may be prescribed, apply to them:
(a) regular servicemen and full-time national servicemen in the Singapore Armed Forces from the time their liability to report for enlistment or service arises until such time as they are lawfully discharged or released;
(b) operationally ready national servicemen from the time that they are ordered to report for enlistment or service, whether they have complied with such order or not, and while in uniform or performing service in the Singapore Armed Forces or the PeopleÂ’s Defence Force pursuant to section 14 of the Enlistment Act (Cap. 93), and while called out for mobilised service pursuant to sections 16 and 17 of that Act or when called out to duty in aid of the civil power;
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So NSmen are only liable under the act when they have been recalled or mobilised. AFAIK, There is no direct prohibition on the joining of a foreign army in the act, unless that army happens to be the enemy. (Look under mutiny, AWOL, and Desertion.)
-- Treason --
SINGAPORE (Penal Code, Chapter VI)
CHAPTER VI
OFFENCES AGAINST THE STATE
Waging or attempting to wage war or abetting the waging of war against the Government. 121. Whoever wages war against the Government, or attempts to wage such war, or abets the waging of such war, shall be punished with death, or with imprisonment for life, and shall also be liable to fine.
Illustration
A joins an insurrection against the Government. A has committed the offence defined in this section.
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Offences against authority. 121B. Whoever compasses, imagines, invests, devises or intends the deprivation or deposition of the President from the sovereignty of Singapore, or the overawing by criminal force of the Government, shall be punished with imprisonment for life, and shall also be liable to a fine.
Abetting offences under section 121A or 121B. 121C. Whoever abets the commission of any of the offences punishable by section 121A or 121B shall be punished with the punishment provided for those offences.
Intentional omission to give information of offences against section 121, 121A, 121B or 121C by a person bound to inform. 121D. Whoever knowing or having reason to believe that any offence punishable under section 121, 121A, 121B or 121C has been committed intentionally omits to give any information respecting that offence which he is legally bound to give, shall be punished with imprisonment for a term which may extend to 7 years, or with fine, or with both.
Collecting arms, etc., with the intention of waging war against the Government. 122. Whoever collects men, arms or ammunition or otherwise prepares to wage war, with the intention of either waging or being prepared to wage war against the Government, shall be punished with imprisonment for life or imprisonment for a term not exceeding 10 years, and shall also be liable to fine.
Concealing with intent to facilitate a design to wage war. 123. Whoever by any act, or by any illegal omission, conceals the existence of a design to wage war against the Government, intending by such concealment to facilitate, or knowing it to be likely that such concealment will facilitate, the waging of such war, shall be punished with imprisonment for a term which may extend to 10 years, and shall also be liable to fine.
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Waging war against any power in alliance or at peace with Singapore. 125. Whoever wages war against the government of any power in alliance or at peace with the Government, or attempts to wage such war, or abets the waging of such war, shall be punished with imprisonment for life, to which fine may be added; or with imprisonment for a term which may extend to 7 years, to which fine may be added, or with fine.
Committing depredation on the territories of any power in alliance or at peace with Singapore.
126. Whoever commits depredation, or makes preparations to commit depredation, on the territories of any power in alliance or at peace with the Government, shall be punished with imprisonment for a term which may extend to 7 years, and shall also be liable to fine and to forfeiture of any property used, or intended to be used, in committing such depredation, or acquired by such depredation.
Receiving property taken by war or depredation mentioned in sections 125 and 126. 127. Whoever receives any property knowing the same to have been taken in the commission of any of the offences mentioned in sections 125 and 126, shall be punished with imprisonment for a term which may extend to 7 years, and shall also be liable to fine and to forfeiture of the property so received.
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Again, deosn;t seem to be a prohibition on the joiining of a foreign army. There are, however, some sections that may be of concern. Eg. When the army you join goes to war against Singapore, or when that army attacks a nation at peace with singapore.
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Need more reserach.